Question

The perimeter of the given quadrilateral ABCD circumscribing a circle is

• A. 32 cm
• B. 62 cm
• C. 48 cm

Answer 1

The correct option is B 62 cm

Let us assume $BQ=\text{x}cm$
Now, $AQ=AB-BQ=(15-\text{x})cm$

By Theorem- Tangents drawn from an external point to the circle are equal in lengths.
$\therefore DS=DP=4cm$,
$CS=CR=12cm$,
$BR=BQ=\text{x}cm$, and
$AP=AQ=(15-\text{x})cm$

Now, perimeter of a quadrilateral $ABCD=AB+BC+CD+AD=AB+(BR+CR)+(CS+DS)+(AP+DP)=15+(\text{x}+12)+(12+4)+\left(\right(15-\text{x})+4)=15+12+12+4+15+4=62cm$

$\therefore$ Perimeter of a quadrilateral $ABCD=62cm$