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

In ΔABC and ΔDAC

∠BAC = ∠ADC (Given in the statement)

∠ACB = ∠ACD (Common angles)

⇒ ΔABC ∼ ΔDAC (AA criterion)

If two triangles are similar, then their corresponding sides are proportional.

⇒ CA / CD = CB / CA

⇒ CA² = CB × CD

Hence, proved.