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Question
In ΔABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:
(i) ΔOMA and ΔOLC
(ii) `"OA"/"OC"="OM"/"OL"`
Solution
We have,
AL ⊥ BC and CM ⊥ AB
In Δ OMA and ΔOLC
∠MOA = ∠LOC [Vertically opposite angles]
∠AMO = ∠CLO [Each 90°]
Then, ΔOMA ~ ΔOLC [By AA similarity]
`therefore"OA"/"OC"="OM"/"OL"` [Corresponding parts of similar Δ are proportional]
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