Question

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

• A. $BC.CD$
• B. $BD.DC$
• C. $BC.BC$
• D. $AD.DC$

Answer 1

The correct option is A $BC.CD$

Given: $\angle ADC=\angle BAC$

In $△BAC$ and $△ADC$,
$\angle ACB=\angle ACD$ .... (common angles)
$\angle BAC=\angle ADC$ .... (Given)
$\therefore △BAC\sim △ADC$ .... (AA simlilarity)
$\Rightarrow \frac{BA}{AD}=\frac{AC}{CD}=\frac{BC}{AC}\Rightarrow \frac{AC}{CD}=\frac{BC}{AC}\Rightarrow A{C}^2=BC.CD$