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 \mathrm{cm}$, find the perimeter of $ △PCD$

Answer 1

Step 1: Given

According to the given details

From an external point $P$, two tangents, $PA$ and $PB$ are drawn to a circle with center $O$.

At a point $E$ on the circle, tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$, respectively and $PA=10\mathrm{cm}$

Step 2: Determine perimeter of $△PCD$

We know that Tangents drawn from an external point to a circle are equal.

$AC=CE$ [Tangents from point $C$]

$ED=DB$ [Tangents from point $D$]

Perimeter of $△PCD=PC+CD+PD$

$$\begin{gathered} =PC+CE+ED+DP \\ =PC+AC+DB+DP\left[\because CE=AC,ED=DB\right] \\ =PA+PB \\ =10+10\left[\because PA=PB=10\mathrm{cm}\right] \\ =20\mathrm{cm} \end{gathered}$$

Therefore, perimeter of $△PCD=20\mathrm{cm}$