Question

Given:• Points U, V, W, and T are points of tangency.• PR = 7• PT = 4• TS = 1• WQ = 2PwSFind the perimeter of quadrilateral PRQS.15161920

Answer 1

From the figure given, a circle UVWT is inscribed in a quadrilateral PRQS;

Thus, the following sides are congruent;

`\begin{gathered} |TP|\cong|UP|=4 \\ |TS|\cong|WS|=1 \\ |WQ|\cong|VQ|=2 \\ |VR|\cong|UR|=x \end{gathered}`

Thus,

`\begin{gathered} |PR|=|UP|+|UR| \\ x=7-4 \\ x=|UR|=|VR|=3 \end{gathered}`

Thus, the perimeter of the quadrilateral PRQS is;

`\begin{gathered} P=|PR|+|RQ|+|QS|+|SP| \\ P=7+3+2+2+1+1+4 \\ P=20 \end{gathered}`

CORRECT OPTION: 20