Question

If a circle is inscribed in a square of side $10$ , so that the circle touches the four sides of the square internally then radius of the circle is

• A. $10$
• B. $5\sqrt{2}$
• C. $10\sqrt{2}$
• D. $5$

Answer 1

The correct option is D $5$

$Letradiusbercm$
$Weknow\text{tangents from a point to the circle are equal}$
$\text{Hence}$
$\text{PD =DQ = r}$
$Given$
$DC=10$
$r+r=10$
$2r=10$
$r=5cm$