How to find the length of a radius - GRE Quantitative Reasoning
Card 0 of 4
"O" is the center of the circle as shown below.
A
---
The radius of the circle
B
---
3
"O" is the center of the circle as shown below.
A
---
The radius of the circle
B
---
3
We know the triangle inscribed within the circle must be isosceles, as it contains a 90-degree angle and fixed radii. As such, the opposite angles must be equal. Therefore we can use a simplified version of the Pythagorean Theorem,
a2 + a2 = c2 → 2r2 = 16 → r2 = 8; r = √8 < 3. (since we know √9 = 3, we know √8 must be less); therefore, Quantity B is greater.
We know the triangle inscribed within the circle must be isosceles, as it contains a 90-degree angle and fixed radii. As such, the opposite angles must be equal. Therefore we can use a simplified version of the Pythagorean Theorem,
a2 + a2 = c2 → 2r2 = 16 → r2 = 8; r = √8 < 3. (since we know √9 = 3, we know √8 must be less); therefore, Quantity B is greater.
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Which point could lie on the circle with radius 5 and center (1,2)?
Which point could lie on the circle with radius 5 and center (1,2)?
A radius of 5 means we need a distance of 5 from the center to any points on the circle. We need 52 = (1 – _x_2)2 + (2 – _y_2)2. Let's start with the first point, (3,4). (1 – 3)2 + (2 – 4)2 ≠ 25. Next let's try (4,6). (1 – 4)2 + (2 – 6)2 = 25, so (4,6) is our answer. The same can be done for the other three points to prove they are incorrect answers, but this is something to do ONLY if you have enough time.
A radius of 5 means we need a distance of 5 from the center to any points on the circle. We need 52 = (1 – _x_2)2 + (2 – _y_2)2. Let's start with the first point, (3,4). (1 – 3)2 + (2 – 4)2 ≠ 25. Next let's try (4,6). (1 – 4)2 + (2 – 6)2 = 25, so (4,6) is our answer. The same can be done for the other three points to prove they are incorrect answers, but this is something to do ONLY if you have enough time.
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A circular fence around a monument has a circumference of 
feet. What is the radius of this fence?
A circular fence around a monument has a circumference of
This question is easy on the whole, though you must not be intimidated by one small fact that we will soon see. Set up your standard circumference equation:
The circumference is 
feet, so we can say:
Solving for 
, we get:
Some students may be intimidated by having 
in the denominator; however, there is no need for such intimidation. This is simply the answer!
This question is easy on the whole, though you must not be intimidated by one small fact that we will soon see. Set up your standard circumference equation:
The circumference is
Solving for
Some students may be intimidated by having
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Circle 
has a center in the center of Square 
.
The area of Square ABCD is 
.
What is the radius of Circle 
?
Circle
The area of Square ABCD is
What is the radius of Circle
Since we know that the area of Square 
is 
, we know 
, where 
is the length of one of its sides. From this, we can solve for 
by taking the square root of both sides. You will have to do this by estimating upward. Therefore, you know that 
is 
. By careful guessing, you can quickly see that 
is 
. From this, you know that the diameter of your circle must be half of 
, or 
(because it is circumscribed). Therefore, you can draw:
Since we know that the area of Square
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