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 = 14 cm, find the perimeter of ΔPCD.

Answer 1

$$\begin{gathered} \text{Given, PA}\text{}\text{and PB are the tangents to a circle with centre O and CD is a tangent at E and PA}=14\text{cm}\text{.} \\ \text{Tangents drawn from an external point are equal.} \\ \therefore \mathit{\text{PA}}\mathit{=}\mathit{\text{PB,CA}}\mathit{=}\mathit{\text{CE}}\text{and}\mathit{\text{DB}}\mathit{=}\mathit{\text{DE}} \\ \text{Perimeter of}△\mathit{\text{PCD}}\mathit{=}\mathit{\text{PC}}\mathit{+}\mathit{\text{CD}}\mathit{+}\mathit{\text{PD}} \\ =(\mathit{\text{PA}}-\mathit{\text{CA}})+(\mathit{\text{CE}}+\mathit{\text{DE}})+(\mathit{\text{PB}}-\mathit{\text{DB}}) \\ =(\mathit{\text{PA}}-CE)+(\mathit{\text{CE}}+\mathit{\text{DE}})+(\mathit{\text{PB}}-\mathit{\text{DE}}) \\ \text{=}(\mathit{\text{PA}}+\mathit{\text{PB}}) \\ \text{=2PA}(\because \text{PA=PB}) \\ \mathit{=}(2\times 14)\text{cm} \\ \text{=28 cm} \\ \therefore \text{Perimeter of}△\mathit{\text{PCD}}=28\text{cm}\text{.} \end{gathered}$$