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

Given that

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

To Prove

 CA2 = CB.CD

Ncert solutions class 10 chapter 6-21

 Proof

From ΔADC and ΔBAC,

∠ADC = ∠BAC (Given)

∠ACD = ∠BCA (Common angles)

∴ ΔADC ~ ΔBAC (From AA similarity criterion)

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

∴ CA/CB = CD/CA

Hence

⇒ CA2 = CB.CD.

Hence, proved.

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