Question

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 in cm.

Answer 1

From the graph, we find some conclusion-

$PA=PB=10$cm

$CE=CA$

$DE=DB$

Perimeter of $\Delta PCD$ is,

$=PC+PD+CD$

$\Rightarrow PC+PD+CE+ED$

$\Rightarrow PC+PD+CA+DB$

$\Rightarrow (PC+CA)(PD+DB)$

$\Rightarrow PA+PB$

$\Rightarrow 10+10$

$\Rightarrow 20$ cm.