In the diagram above, line PQ is tangent to the circle, and the measure of arc PR is

[BTGmoderatorDC]

In the diagram above, line PQ is tangent to the circle, and the measure of arc PR is 70°. What is the measure of ∠PQR?

A. 15°
B. 20°
C. 25°
D. 30°
E. 35°


OA B

Source: Magoosh

[Brent@GMATPrepNow]

c3_img3.png

In the diagram above, line PQ is tangent to the circle, and the measure of arc PR is 70°. What is the measure of ∠PQR?

A. 15°
B. 20°
C. 25°
D. 30°
E. 35°


OA B

Source: Magoosh

There's a real nice Circle Property rule that says: A line tangent to a circle will be perpendicular to the line passing through the center and the point of tangency
This means ∠OPQ = 90°
We are also told that ∠OPR = 70°

Since all three angles in a triangle must add to 180°, we can conclude that ∠PQR = 20°

Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

c3_img3.png

In the diagram above, line PQ is tangent to the circle, and the measure of arc PR is 70°. What is the measure of ∠PQR?

A. 15°
B. 20°
C. 25°
D. 30°
E. 35°


OA B

Source: Magoosh

While we are not told that it is so, we assume that O is the center because otherwise, the answer cannot be determined from the given information.

Since arc PR = 70 degrees, then the intercepted central angle (angle ROP) is also 70 degrees. Furthermore, since line PQ is tangent to the circle, angle OPQ = 90 degrees. Therefore, angle PQR = 180 - 70 - 90 = 20 degrees.

Answer: B