Q) D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC, prove that CA² = CB.CD

Ans: 

Let’s draw the diagram with triangle ABC.

Let’s compare Δ CBA with Δ CAD

∠ ADC = ∠ BAC       (given)

∠ C = ∠ C                (common angle)

Δ CBA ~ Δ CAD (by AA similarity)

Hence, corresponding sides will be proportional

CA² = CB.CD…… Hence Proved