Question

In the figure, $△ABC$ is a right angled triangle with $\angle B={90}^{\circ }$. If BD is perpendicular to AC, then $AC\times AD$ = ____.

• A. $A{D}^2$
• B. $A{B}^2$
• C. $B{D}^2$
• D. $D{C}^2$

Answer 1

The correct option is B $A{B}^2$

Given: $\angle ABC={90}^{\circ }$
BD is perpendicular to AC

$\Rightarrow \angle BDA={90}^{\circ }$

In $△ABC$ and $△ADB$,

$\angle ABC=\angle BDA={90}^{\circ }$ (given)

$\angle BAD=\angle BAC$ (common in both triangles)

$\therefore △ABC\sim △ADB$ (by AA similarity criterion)

$\Rightarrow \frac{AB}{AC}=\frac{AD}{AB}$
(corresponding sides of similar triangles are in same ratio)

$\Rightarrow A{B}^2=AC\times AD$