Two chordsKVandQRof circleOare perpendicular at ointP, withPQ= 6 andPR= 8. If the radius of circleOis √65, findKPandPV.

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- Nov 12th 2008, 09:13 AMbearej50please help
Two chords

*KV*and*QR*of circle*O*are perpendicular at oint*P*, with*PQ*= 6 and*PR*= 8. If the radius of circle*O*is √65, find*KP*and*PV*. - Nov 13th 2008, 07:26 AMred_dog
Let $\displaystyle OM\perp RQ$ and $\displaystyle ON\perp KV$.

$\displaystyle RQ=14\Rightarrow MQ=7\Rightarrow ON=MP=MQ-PQ=7-6=1$

In the triangle OMQ: $\displaystyle OM=\sqrt{OQ^2-MQ^2}=\sqrt{65-49}=\sqrt{16}=4\Rightarrow PN=4$

In the triangle ONK: $\displaystyle KN=\sqrt{OK^2-ON^2}=\sqrt{65-1}=8$

Then $\displaystyle KP=KN-PN=8-4=4$ and $\displaystyle PV=KV-KP=16-4=12$ - Nov 13th 2008, 08:02 AMlmcph24
Red dog your a genius any chance you can help with my problem?

http://www.mathhelpforum.com/math-he...arger-one.html - Nov 13th 2008, 08:36 AMbearej50
thank you very much red dog!