D is a point on the side BC of a triangleABC such that ∠ ADC = ∠ BAC. Show that CA 2 = CB.CD

Question

D is a point on the side BC of a triangleABC such that &#x2220; ADC = &#x2220; BAC. Show that CA 2 = CB.CD

Philoid · Accepted Answer

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