In figure, if AB || DC and AC, PQ intersect each other at the point O. Prove that OA . CQ = OC . AP
AC and PQ intersect each other at the point O and AB || DC.
From ∆AOP and ∆COQ,
∠AOP = ∠COQ ......[Since they are vertically opposite angles]
∠APO = ∠CQO .....[Since, AB || DC and PQ is transversal, the angles are alternate angles]
∴ ∆AOP ∼ ∆COQ ......[Using AAA similarity criterion]
Then, since, corresponding sides are proportional
`(OA)/(OC) = (AP)/(CQ)`
OA × CQ = OC × AP
Concept: Similarity of Triangles
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