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In the diagram above, line PQ is tangent to the circle, and the measur

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Bunuel
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In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 08:27
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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°


Kudos for a correct solution.
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ynaikavde
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 08:54
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angle at O is 70 and angle at P= 90 using right angle pythagoras theorem we get angle at Q= 20 answer B
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 19:15
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Bunuel wrote:
Attachment:
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°


Kudos for a correct solution.


triangle OPQ is a right triangle.

so 180-90-70=20

Answer B
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 19:26
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Hi All,

For a multi-shape Geometry question, this prompt is remarkably straight-forward, but only if you know the rule for tangent lines.....

Show Spoiler
When a line is tangent to a circle, the angle that forms when the radius of the circle touches the tangent line is ALWAYS 90 degrees


With that knowledge, you can make quick work of this prompt.

GMAT assassins aren't born, they're made,
Rich
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chetan2u
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 19:36
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Bunuel wrote:
Attachment:
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°


Kudos for a correct solution.


a tangent always creates a 90 degree angle at the center of circle .. so we have a triangle with two angles as 70 and 90..
third angle will be 20..
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  02 Mar 2015, 22:05
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Answer = B = 20

Refer diagram below:

Attachment:
c3_img3.png
c3_img3.png [ 12.26 KiB | Viewed 6069 times ]


Tangent line makes a angle of 90 degrees.

∠PQR = 90-70 = 20
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Bunuel
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  08 Mar 2015, 14:11
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Bunuel wrote:
Attachment:
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°


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

First of all, since the measure of arc PR is 70°, we know the angle at the center, ∠POR, must also be 70°. We know that ∠OPQ = 90°, because PQ is a tangent line. Now look at triangle OPQ. We know that the three angles in that triangle must add up to 180°.
∠POR + ∠ OPQ + ∠ PQR = 180°
70° + 90° + ∠ PQR = 180°
160° + ∠ PQR = 180°
∠ PQR = 180° – 160° = 20°.

Answer = B
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BrentGMATPrepNow
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In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  Updated on: 17 May 2021, 07:22
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Bunuel wrote:
Attachment:
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°


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

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Originally posted by BrentGMATPrepNow on 18 Dec 2019, 07:39.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:22, edited 1 time in total.
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  18 Dec 2019, 07:52
Basically a radius is always perpendicular to a tangent (property of a tangent).

The angle is 90°. ∠OPQ = 90°
Given, ∠OPR = 70°.
Therefore in 3rd angle of the ΔOPQ, ∠PQR = 20°

Ans: B
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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink] New post  23 Dec 2019, 18:50
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Bunuel wrote:
Attachment:
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°


Kudos for a correct solution.


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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Re: In the diagram above, line PQ is tangent to the circle, and the measur [#permalink]
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