In figure , if `ABabs()DC` and AC, PQ intersect each other at the point O. Prove that OA.CQ=OC.AP.

Explanation

Given AC and PQ intersect each other at the point O and AB`abs()`DC.
To prove OA.CQ=OC.AP
Proof In `DeltaAOP and DeltaCOQ` `angleAOP=angleCOQ` [vertically opposite angle]
`angleAPO=angleCQO`
[Since, AB`abs()`DC and PQ is transversal, so alternate angles]
`therefore DeltaAOP~DeltaCOQ` [by AAA similarity angles]
Then, `(OA)/(OC)=(AP)/(CQ)` {Since, corresponding sides are proportioonal]
`rArr OAcdotCQ=OCcdotAP` Hence proved.