Question

In ΔABC; BM ⊥ AC and CN ⊥ AB; show that:

`(AB)/(AC) = (BM)/(CN) = (AM)/(AN)`

Answer 1

In ΔABM and ΔACN,

∠AMB = ∠ANC  ...(BM ⊥ AC and CN ⊥ AB)

∠BAM = ∠CAN  ...(Common angle)

`=>` ΔABM ∼ ΔACN  ...(AA criterion for similarity)

`=> (AB)/(AC) = (BM)/(CN) = (AM)/(AN)`