D is a point on the side BC of a triangleABC such that ∠ ADC = ∠ BAC. Show that CA² = CB.CD

In ΔADC and ΔBAC,

∠ADC = ∠BAC (Given)

∠ACD = ∠BCA (Common angle)

ΔADC ΔBAC (By AA similarity)

We know that corresponding sides of similar triangles are in proportion

Hence,

CA² = CB * CD