Question

In the given figure, in ∆ABC, point D on side BC is such that, ∠BAC = ∠ADC. Prove that, CA² = CB × CD.

Answer 1

Given: In ΔBAC and ΔADC,

∠BAC ≅ ∠ADC    ...(Given)

∠ACB ≅ ∠DCA    ...(Common angle)

∴ ΔBAC ∼ ΔADC    ...(AA test of similarity)

∴ `"CA"/"CD" = "CB"/"CA"`    ...(Corresponding sides of similar triangles are in proportion)

∴ CA² = CB × CD.