Question

A circle is inscribed in a quadrilateral ABCD in which $\angle B={90}^o$. If $AD=23cm$, $AB=29cm$ and $DS=5cm$. Find the radius of the circle.

• A. $11$ cm
• B. $13$ cm
• C. $9$ cm
• D. None of these

Answer 1

Answer: (A)

$11$ cm

$AS$ and $AP$ are tangents drawn to the circle at $A$

$⟹AS=AP$

Similarly

$BP=BQ$

$QC=CR$

$RD=DS$

Given

$AD=23$

$⟹AS+SD=23$

$AS=23–5=18=AP$

$AB=29⟹AP+BP=29$

$⟹18+BP=29⟹BP=11cm$

Now consider rectangle $PBQO$

$PB–BQ,OP=OQ=radius$

$\angle PBQ=90$

WKT

$OP\perp BP$ and $OQ\perp BQ$

Since radius is perpendicular to tangent at point of contact

$⟹$ All the angles are 90 degree and adjacent sides are equal

So, It is a square

$⟹r=BP=11cm$