D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Show that CA² = CB.CD

Solution:

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

⇒ CA² = CB × CD

Hence, proved.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 6

Video Solution:

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. Show that CA² = CB.CD

NCERT Solutions Class 10 Maths Chapter 6 Exercise 6.3 Question 13

Summary:

D is a point on the side BC of a triangle ABC such that ∠ADC = ∠ BAC. We have proved that CA² = CB.CD.

☛ Related Questions:

• E is a point on the side AD produced of a parallelogram ABCD and BE intersect CD at F. Show that ΔABE ~ ΔCFB.
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