D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC.
CA2 = CB.CD
From ΔADC and ΔBAC,
∠ADC = ∠BAC (Given)
∠ACD = ∠BCA (Common angles)
∴ ΔADC ~ ΔBAC (From AA similarity criterion)
We know that the corresponding sides of similar triangles are in proportion.
∴ CA/CB = CD/CA
⇒ CA2 = CB.CD.