Lenght of minor arc PQ

[anousha]

Hi,

This is a question from GMAT Prep Practice Test 1. Could someone please explain how to solve this? What assumptions can be made?

here is image url http://www.postimage.org/image.php?v=Ts12gCqi

Thank you!
Anousha

[ramesh.krish.85]

since angle PRO = 35 we know that angle QPR = 35 [alternate angles are equal].

Angle made by PQ at the center = 360 - [Angle made by PO at center + Angle made by QR at center + angle made by OR at center]

Angle made by PO at center = 2(35) = 70 [angle made by an arc at center = twice the angle made by arc at any pt on the circunference of the circle]

Angle made by QR at center = 2(35) = 70 [Same logic as above]

angle made by OR at center = 180 [we know it is the diameter]

Angle made by PQ at the center = 360 - [70 + 70 + 180] = 40

length of the arc PQ = (40/360) * 2 Pi 9 = 2 Pi

Please let me know if there is an easier way to solve this problem

[anousha]

ahhh now I see. Thank you Ramesh for the easy to follow explanation!

[StaceyKoprince]

thanks ramesh!!