Question

D is a point on the side BC of a triangle ABC such that angleADC=angleBAC. Show that CAsquare=CB×CD.

Answer 1

In ΔADC and ΔBAC,  

∠ADC = ∠BAC (Given)  

∠ACD = ∠BCA (Common angle)  

∴ ΔADC ~ ΔBAC (By AA similarity criterion)  

We know that corresponding sides of similar triangles are in proportion.

∴ CA/CB =CD/CA

⇒ CA2 = CB.CD.