Q5 of 57 Page 66

In figure, if AB‖DC and AC, PQ intersect each other at the point 0. Prove that 0A. CQ = OC.AP.

Given,

AC and PQ intersect each other at the point O and AB‖DC.


in ∆AOP and ∆COQ,


∠AOP = ∠COQ [vertically opposite angles]


∠APO = ∠CQO [since, AB‖DC and PQ is transversal, so alternate angles]


∴ ∆AOP ∼ ∆COQ [by AAA similarity criterion]


Then, OA/OC = AP/CQ


[since, corresponding sides are proportional]


⇒ OA × CQ = OC × AP


Hence Proved.


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