Ex.6.3 Q13 Triangles Solution - NCERT Maths Class 10

Go back to  'Ex.6.3'

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

\[\Rightarrow \frac{C A}{C D}=\frac{C B}{C A}\]

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