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

Asked by Abhisek | 1 year ago |  89

##### Solution :-

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

∠ACD = ∠BCA (Common angles)

ΔADC ~ ΔBAC (AA similarity criterion)

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

$$\dfrac{CA}{CB}=\dfrac{CD}{CA}$$

⇒ CA2 = CB.CD.

Hence, proved.

Answered by Pragya Singh | 1 year ago

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