Question

From an external point $P$, tangents $PA$ and $PB$ are drawn to a circle with centre $O$. If $CD$ is the tangent to the circle at a point $E$ and $PA=14cm$, find the perimeter of $△PCD$.

Answer 1

Given : PA and PB are tangent to the circle with centre O.

CD is a tangent to the circle at E which intersect PA and PB in C and D respectively and PA=14 cm

Length of tangents drawn from as external point to a circle are equal.

$\therefore PA=PB=14cm$

$CA=CE$

$DB=DE$

Now perimeter of $△PCD=PC+CD+PD$

$=PC+(CE+ED)+PD$

$=PC+(CA+DB)+PD$

$=(PC+CA)+(DB+PD)$

$=PA+PB$

$=14+14$

$=28cm$