Question

In triangle ABC,D is a point on side BC that angle ADC=BAC Prove that CA^2=CB.CD

Answer 1

assume ΔBAC and ΔADC
∠ADC = ∠BAC as given
∠C = ∠C 
so,  ΔBAC ~ ΔADC 
 AB/AD= CB/CA= CA/CD

as CB/CA= CA/CD

we can write as CA.CA= CB. CD