DSQ: Calculating the length of a chord

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating the length of a chord

Questions

8

1

Chords

Note: Figure NOT drawn to scale

Refer to the above figure. Is $\Delta ABC$ an isosceles triangle?

Statement 1: $\widehat{ABC}$ and $\widehat{BCA}$ have equal length.

Statement 2: $\widehat{ABC}$ and $\widehat{BCA}$ have equal degree measure.

2

Chord

Note: Figure NOT drawn to scale

Examine the above figure. True or false: $\overline{AB} \cong \overline{YZ}$ .

Statement 1: $\overline{XY} \cong \overline{BC}$

Statement 2: $\angle ABC \cong \angle XYZ$

3

Chord

Note: Figure NOT drawn to scale.

Examine the above figure. True or false: $\overline{AB} \cong \overline{CD}$ .

Statement 1: Arc $\widehat{CAB}$ is longer than arc $\widehat{ACD}$ .

Statement 2: Arc $\widehat{ABD}$ is longer than arc $\widehat{CDB}$ .

4

Chord

Note: Figure NOT drawn to scale.

Examine the above diagram. True or false: $\overline{AB} \cong \overline{CD}$ .

Statement 1: is the midpoint of $\overline{BD}$ .

Statement 2: is the midpoint of $\overline{AC}$ .

5

Chord

Note: Figure NOT drawn to scale.

Examine the above figure. True or false: $\overline{AB} \cong \overline{CD}$ .

Statement 1: Arcs $\widehat{ AB}$ and $\widehat{ CD}$ have the same length.

Statement 2: Arcs $\widehat{ADB}$ and $\widehat{CBD}$ have the same degree measure.

6

Chord

Note: Figure NOT drawn to scale

Examine the above figure. True or false: $\overline{AB} \cong \overline{YZ}$ .

Statement 1: $\overline{XY} cong \overline{BC}$

Statement 2: $\angle ABC cong \angle XYZ$

7

Chord

Note: Figure NOT drawn to scale.

In the above figure, is the center of the circle, and $\Delta OAB$ is equilateral. Give the length of Give the length of chord $\overline{AB}$ .

Statement 1: The circle has area $64 \pi$ .

Statement 2: $\Delta OAB$ has perimeter .

8

Chord

Note: Figure NOT drawn to scale.

Give the length of chord $\overline{AB}$ .

Statement 1: Minor arc $\widehat{AB}$ has length $8 \pi$ .

Statement 2: Major arc $\widehat{ACB}$ has length $16 \pi$ .

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