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 \(\Delta ABC\) such that \(\angle ADC\) \(=\) \(\angle BAC\). Show that \(\,C{{A}^{2}}=CB.CD\) .

Diagram

 Video Solution
Triangles
Ex 6.3 | Question 13

Text Solution

Reasoning:

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

Steps:

In \(\Delta ABC\) and \(\Delta DAC\)

\[\begin{align} & \angle BAC=\angle ADC \\  & \text{(Given in the statement)}\\\\ & \angle ACB=\angle ACD\\  & \text{(Common angles)} \\\\  \Rightarrow \quad&\Delta ABC \sim \Delta DAC \\ &  \text{(AA criterion)} \end{align}\]

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

\[\begin{align} \Rightarrow \quad\frac{C A}{C D}&=\frac{C B}{C A}\\\Rightarrow \quad C A^{2}&=C B \cdot C D\end{align}\]