Question

$\text{If D is a point on the side BC of}\Delta ABC\text{such that}\angle ADC=\angle BAC,\text{then}C{A}^2\text{will be equal to}$

• A. $\frac{CB}{CD}$
• B. $\frac{C{B}^2}{CD}$
• C. $\frac{CB}{4CD}$
• D. $CB\times CD$

Answer 1

The correct option is D $CB\times CD$

$\text{In}\Delta ABC\text{and}\Delta DAC$,

$\angle ADC=\angle BAC\text{(Given)}$

$\angle C=\angle C\text{(Common angle)}$

$\therefore \Delta ABC\sim \Delta DAC\text{(By AA Similarity)}$

$\Rightarrow \frac{AB}{DA}=\frac{BC}{AC}=\frac{AC}{DC}$
$\text{(Corresponding sides of similar}\text{triangles)}$

$\Rightarrow \frac{CB}{CA}=\frac{CA}{DC}$

$\Rightarrow C{A}^2=CB\times CD$