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
Circles and tangents
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By Circle Theorem, triangle PQO is a 306090 triangle where Angle QPO = 60 degrees
Hypotenuse PO = 9/cos60 = 9/0.5 = 18
Hypotenuse PO = 9/cos60 = 9/0.5 = 18
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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 306090 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
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 306090 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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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/gmatgeometry?id=863
Cheers,
Brent
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/gmatgeometry?id=863
Cheers,
Brent