## Circles and tangents

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### Circles and tangents

by sukriti2hats » Fri Jun 13, 2014 1:34 am
Looking for a different strategy..

In the given figure, if PQ=9 cm and O is the centre of the circle, then find the length of PO when angle QOR= 60, and PQO =PRO=90.

A) 18 cm
B) 28 cm
C) 13.5 cm
D) 9âˆš3/2 cm
E) 15âˆš3/2 cm

OA: A
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by Mathsbuddy » Fri Jun 13, 2014 5:35 am
By Circle Theorem, triangle PQO is a 30-60-90 triangle where Angle QPO = 60 degrees

Hypotenuse PO = 9/cos60 = 9/0.5 = 18

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by GMATinsight » Fri Jun 13, 2014 7:02 am
Hi Sukriti,

PQ = 9, Angle PQO = 90, angle QOP = (1/2)* angle QOR = (1/2)*60 = 30 degrees

Therefore angle QOP = 30 degrees therefore angle QPO = 60 degrees not use 30-60-90 property
The ratio of sides is 1:Sqrt3:2

QP = 9, QO = 9(Sqrt3) and PO = 289 = 18 ANSWER

Refer the image attached for figure
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by [email protected] » Fri Jun 13, 2014 11:38 am
I'd like to mention that this question is made much more difficult by the MISLEADING diagram, which is WAYYYY out of scale. We're told that âˆ QOR = 60Âº, but the angle on the diagram is closer to 180Âº than to 60Âº

Please note that the geometric figures in GMAT PROBLEM SOLVING questions are drawn proportionately unless the question explicitly states that the figure is not drawn to scale.

For more about this important feature, you can watch our free video titled "Assumptions and Estimation on the GMAT": https://www.gmatprepnow.com/module/gmat-geometry?id=863

Cheers,
Brent

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