# D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Show that CA^{2} = CB.CD

**Solution:**

As we know that if two triangles are similar, then their corresponding sides are proportional.

In ΔABC and ΔDAC

∠BAC = ∠ADC (Given in the statement)

∠ACB = ∠ACD (Common angles)

⇒ ΔABC ∼ ΔDAC (AA criterion)

If two triangles are similar, then their corresponding sides are proportional

⇒ CA / CD = CB / CA

⇒ CA^{2} = CB × CD

**Video Solution:**

## D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Show that CA^{2} = CB.CD

### NCERT Solutions Class 10 Maths - Chapter 6 Exercise 6.3 Question 13:

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Show that CA^{2} = CB.CD

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Hence proved that CA^{2} = CB.CD