In figure , if `Ababs()DC` and AC, PQ interrest each other at the poin – InterviewSolution

1.	In figure , if `Ababs()DC` and AC, PQ interrest each other at the point 0. Prove that OA.CQ=OC.AP.
Answer» 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.

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