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