# Ex.6.3 Q13 Triangles Solution - NCERT Maths Class 10

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## Question

$$D$$ is a point on the side $$BC$$ of a $$\triangle ABC$$ such that $$\angle ADC$$ $$=$$ $$\angle BAC$$. Show that $$\,C{{A}^{2}}=CB.CD$$ .

Diagram

## Text Solution

Reasoning:

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

Steps:

In $$\Delta ABC$$ and $$\Delta DAC$$

$$\angle BAC=\angle ADC$$   (Given in the statement)

$$\angle ACB=\angle ACD$$  (Common angles)

$$\Rightarrow \Delta ABC \sim \Delta DAC$$ (AA criterion)

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

$\Rightarrow \frac{C A}{C D}=\frac{C B}{C A}$

\begin{align} {\Rightarrow C A^{2}=C B \cdot C D}\end{align}

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