Question

In the figure, tangents $PA$ and $PB$ are drawn to a circle with centre $O$ from an external point $P$. If $CD$ is a tangent to the circle at $E$ and $AP=15cm$, find the perimeter of $△PCD$

Answer 1

We know that the lengths of the two tangents from an exterior point to a circle are equal.

$\therefore CA=CE,DB=DE$ and $PA=PB$.

Now, the perimeter of $△PCD=PC+CD+DP$

$=PC+CE+ED+DP$

$=PC+CA+DB+DP$

$=PA+PB=2PA$ $(PB=PA)$

Thus, the perimeter of $△PCD=2\times 15=30cm$.