Question

In a right angled triangle $ABC,AD$ is perpendicular to the hypotenuse $BC$ then $A{D}^2$ is equal to:

• A. $AB\cdot BD$
• B. $AC\cdot DC$
• C. $BD\cdot DC$
• D. $AB\cdot AC$

Answer 1

The correct option is C $BD\cdot DC$

$AD$ is $\perp$ to $BC$ where $BC$ is hypotenuse.

In $△ABC$,

${AB}^2+{AC}^2={BC}^2$

The area of triangle is either $\frac{1}{2}AB\times AC$ or $\frac{1}{2}BC\times AD$

When we equate both,

$AB\times AC=BC\times AD$

The perpenidcular $AD$ divides the base $BC$ into parts.

$\therefore {AD}^2=BD\times DC$