Question

Question 3
From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

Answer 1

Two tangents $PA$ and $PB$ are drawn to a circle with center $O$ from an external point P.

Perimeter of $△$ $PCD$ =$PC+CD+DP$

$△$$PCD$ = $PC+CE+ED+DP$
$△$$PCD$ = $PC+AC+DB+DP$
$△$$PCD$ = $PA+PB$

[ $\because$ $CE$ =$ACED$ = $DBPA$ = $PB$ tangents drawn from external point to a circle are equal]
$△$$PCD$ = $2PA$= $2\left(10\right)$
$△$$PCD$ =$20$ cm
Hence, the perimeter of the triangle $PCD$ is $20$ cm