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"`

Answer 1

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]