Question

In the given figure, quadrilateral $ABCD$ is circumscribed. The circle touches the sides $AB,BC,CD,DA$ at $P,Q,R,S$ respectively. If $AP=9cm,BP=7cm,CQ=5cm,DR=6cm$, find the perimeter of quad. $ABCD$

• A. $54cm$
• B. $44cm$
• C. $24cm$
• D. $64cm$

Answer 1

Answer: (A)

$54cm$

$ABCD$ is a quadrilateral and let $O$ be the center of the circle inscribed in the quadrilateral.
$AB$, $BC$, $CD$ and $AD$ are the tangent to the circle at $P$, $Q$, $R$ and $S$, $AP=9$, $PB=7$, $QC=5$ and $DR=6$
We know that the lengths of the two tangents from a point to circle are equal.
Thus, $AP=AS=9$ cm
$BP=BQ=7$ cm
$CQ=CR=5$ cm
$DR=DS=6$ cm
Perimeter of quadrilateral $ABCD=AB+BC+CD+AD$
$=AP+BP+BQ+CQ+CR+DR+DS+AS$
$=9+7+7+5+5+6+6+9$
$=54$ cm