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Question

In figure, if ABIIDC and AC, PQ intersect each other at the point O. Prove that OA.CQ = OC.AP.


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Solution

Given AC and PQ intersect each other at the point O and AB II DC.
To prove, OA.CQ = OC. AP
Proof in ΔAOP and ΔCOQ, AOP=COQ [vertically opposite angles]
[since, AB II DC and PQ is transversal, so alternate angles]
ΔAOPΔCOQ [by AAA similarity criterion]
Then, OAOC=APCQ [since, corresponding sides are propotion]
OA.CQ = OC.AP

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