Question

A circle touches sides AD and CD of rectangle ABCD at P and Q, respectively. If the length of the perpendicular from B to PQ is $10$ units, then area of rectangle is

• A. $25$
• B. $50$
• C. $75$
• D. $100$

Answer 1

The correct option is D $100$

Given, $BE=10$

$AD$ and $DC$ touches the circle

$\angle BPQ=\angle BQC$

and $\angle APB=\angle PQB$

also $△BQC$ and $△EPB$ are similar

and $△APB$ and $△EQB$ are similar

$\frac{BC}{BE}=\frac{BQ}{BP}=\frac{BE}{AB}AB\times BC={\left(BE\right)}^2={\left(10\right)}^2=100$