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

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by BTGmoderatorDC » Wed Mar 18, 2020 5:30 pm

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

by Brent@GMATPrepNow » Thu Mar 19, 2020 5:14 am
BTGmoderatorDC wrote: ↑
Wed Mar 18, 2020 5:30 pm
 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

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

by Scott@TargetTestPrep » Sat Mar 21, 2020 3:09 pm
BTGmoderatorDC wrote: ↑
Wed Mar 18, 2020 5:30 pm
 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

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