In the diagram above, line $PQ$ is tangent to the circle,

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Fri Dec 13, 2019 11:11 am

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

A. $15Â°$
B. $20Â°$
C. $25Â°$
D. $30Â°$
E. $35Â°$

[spoiler]OA=B[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Fri Dec 13, 2019 11:11 am

dsan6422: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Dec 12, 2019 4:55 pm

by dsan6422 » Mon Dec 16, 2019 6:04 pm

Hope this helps.

https://youtu.be/BPil_CBN5J4

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Pyunika: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Nov 30, 2019 9:22 am

by Pyunika » Tue Dec 17, 2019 10:52 am

angle p makes 90 degree since it is the tangent to the circle.
angle r is given as 70 degree
and sum of all the angles in the triangle should be 180. thus angle pqr equals 20 degree

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 18, 2019 6:20 am

M7MBA wrote:

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

A. $15Â°$
B. $20Â°$
C. $25Â°$
D. $30Â°$
E. $35Â°$

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 âˆ OPQ = 90Â°
We are also told that âˆ OPR = 70Â°

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

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jan 01, 2020 6:43 pm

M7MBA wrote:

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

A. $15Â°$
B. $20Â°$
C. $25Â°$
D. $30Â°$
E. $35Â°$

[spoiler]OA=B[/spoiler]

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

Scott Woodbury-Stewart
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[email protected]

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