Question

In Fig., a circle is inscribed within a quadrilateral $ABCD$. Given that $BC=38cm,BQ=27cm$ and $DC=25cm$ and that $AD$ is perpendicular to $DC$. The radius of the circle is:

• A. $10cm$
• B. $14cm$
• C. $8cm$
• D. $12cm$

Answer 1

The correct option is B $14cm$

$\because$ Lengths of tangents drawn from an external point to a circle are equal.

$\therefore BQ=BR=27$ cm

Let $x$ be the radius of the circle

$\therefore OP=OS=PD=x$

Now,

$CR=BC-BR$

$=38-27=11$ cm

Now $CS=CR=11$ cm

[$\because$ Length of tangents from an external point to a circle are equal]

$\therefore DS=CD-CS$

$=25cm-11$ cm

$=14$ cm

But $DS=OP=x=14$ cm.

Hence radius $=OP=14$ cm,