Construct Tangent Lines from Outside a Circle: CCSS.Math.Content.HSG-C.A.4 - Common Core: High School - Geometry
Card 0 of 13
Construct a line that is tangent to a point on the circle and passes through the point 
.
Construct a line that is tangent to a point on the circle and passes through the point 
To construct a line that is tangent to a point on the circle and passes through the point 
, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.
Constructing the first potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point 
to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.
To construct a line that is tangent to a point on the circle and passes through the point 
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.
Constructing the first potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point 
Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.
Compare your answer with the correct one above
Construct a line that is tangent to a point on the circle and passes through the point 
.
Construct a line that is tangent to a point on the circle and passes through the point 
To construct a line that is tangent to a point on the circle and passes through the point 
, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.
Constructing the second potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point 
to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.
To construct a line that is tangent to a point on the circle and passes through the point 
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the top half of the circumference while the other potential line would touch the circle on the bottom.
Constructing the second potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point 
Of the other answer choices, two options contain lines that are secant to the circle meaning that the line intersects the circle at point two points thus, those options are not tangent. The other two lines do not intersect nor touch the circle therefore they are not considered tangent either.
Compare your answer with the correct one above
Calculate a point that is tangent to the circle 
and passes through the origin.
Calculate a point that is tangent to the circle
To construct a line that is tangent to a point on the circle and passes through the origin, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at 
and the radius is 
.
Therefore, the center is located at 
and the radius is three. Plotting the circle and tangent line to the origin results in the following.
To construct a line that is tangent to a point on the circle and passes through the origin, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at
Therefore, the center is located at
Compare your answer with the correct one above
Calculate a point that is tangent to the circle 
and passes through the origin.
Calculate a point that is tangent to the circle
explain
explain
Compare your answer with the correct one above
Calculate a point that is tangent to the circle and passes through the point 
.
Calculate a point that is tangent to the circle
To construct a line that is tangent to a point on the circle and passes through the point 
, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at and the radius is .
Therefore, the center is located at and the radius is three. Plotting the circle and tangent line to the point 
results in the following.
Therefore, the point on the circle that creates a tangent line, 
.
To construct a line that is tangent to a point on the circle and passes through the point
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at
Therefore, the center is located at
Therefore, the point on the circle that creates a tangent line,
Compare your answer with the correct one above
Calculate a point that is tangent to the circle and passes through the point 
.
Calculate a point that is tangent to the circle
To construct a line that is tangent to a point on the circle and passes through the point 
, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at and the radius is .
Therefore, the center is located at and the radius is three. Plotting the circle and tangent line to the point 
results in the following.
Therefore, the point on the circle that creates a tangent line with the point given is 
.
To construct a line that is tangent to a point on the circle and passes through the point
Given the equation of the circle,
the center and radius of the circle can be determined.
The center is located at
Therefore, the center is located at
Therefore, the point on the circle that creates a tangent line with the point given is
Compare your answer with the correct one above
Construct a line that is tangent to a point on the circle and passes through the point plotted outside the circle.
Construct a line that is tangent to a point on the circle and passes through the point plotted outside the circle.
To construct a line that is tangent to a point on the circle and passes through the point outside the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the left half of the circumference while the other potential line would touch the circle on the right half.
Constructing a potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point outside the circle to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
To construct a line that is tangent to a point on the circle and passes through the point outside the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the left half of the circumference while the other potential line would touch the circle on the right half.
Constructing a potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point outside the circle to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
Compare your answer with the correct one above
Determine whether the statement is true or false.
The line is tangent to the circle.
Determine whether the statement is true or false.
The line is tangent to the circle.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Looking at the image, it is seen that the line only touches the circle once therefore, the line is tangent to the circle. Thus this statement is true.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Looking at the image, it is seen that the line only touches the circle once therefore, the line is tangent to the circle. Thus this statement is true.
Compare your answer with the correct one above
Construct a line that is tangent to the circle.
Construct a line that is tangent to the circle.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle one possible line would touch the circle is as follows.
Thus resulting in a tangent line to the circle.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle one possible line would touch the circle is as follows.
Thus resulting in a tangent line to the circle.
Compare your answer with the correct one above
Construct a line that is tangent to a point on the circle and passes through the point plotted outside the circle.
Construct a line that is tangent to a point on the circle and passes through the point plotted outside the circle.
To construct a line that is tangent to a point on the circle and passes through the point outside the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the left half of the circumference while the other potential line would touch the circle on the right half.
Constructing a potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point outside the circle to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
To construct a line that is tangent to a point on the circle and passes through the point outside the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Using the plotted circle and the given point, two potential lines can be drawn that will touch the circle at one point. One possible line would touch the circle on the left half of the circumference while the other potential line would touch the circle on the right half.
Constructing a potential tangent line, a point can be plotted on the circle as follows.
From here, connect the given point outside the circle to the point on the circle with a straight line. Thus resulting in a tangent line to the circle.
Compare your answer with the correct one above
Determine whether the statement is true or false.
Given a circle, a tangent line to the circle can be constructed if it intersects the circle at two points.
Determine whether the statement is true or false.
Given a circle, a tangent line to the circle can be constructed if it intersects the circle at two points.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Therefore, by definition the statement is false.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Therefore, by definition the statement is false.
Compare your answer with the correct one above
Determine whether the statement is true or false.
A tangent line to the circle can be constructed between the point at 
and a point on the circle.
Determine whether the statement is true or false.
A tangent line to the circle can be constructed between the point at 
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Constructing the tangent line results in the following image,
Therefore, this statement is true.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Constructing the tangent line results in the following image,
Therefore, this statement is true.
Compare your answer with the correct one above
Determine whether the statement is true or false.
The line is tangent to the circle.
Determine whether the statement is true or false.
The line is tangent to the circle.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Therefore, looking at the graph
it is seen that the line only intersects the circle once. Thus, the statement "The line is tangent to the circle." is true.
To construct a line that is tangent to a point on the circle, recall what it means for a line to be "tangent". A line that is tangent to a point on a circle means that the line will only touch the circle at that specific point.
Therefore, looking at the graph
it is seen that the line only intersects the circle once. Thus, the statement "The line is tangent to the circle." is true.
Compare your answer with the correct one above