**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 Δ *PCD*.

**Solution:**

Let us first put the given data in the form of a diagram.

It is given that PA = 14cm. we have to find the perimeter of.

Perimeter of is *PC + CD + PD*

Looking at the figure we can rewrite the equation as follows.

Perimeter of is *PC + CE + ED + PD* ……(1)

From the property of tangents we know that the length of two tangents drawn to a circle from the same external point will be equal. Therefore,

*CE =CA*

*ED =DB*

Replacing the above in equation (1), we have,

Perimeter of as *PC + CA + DB + PD*

By looking at the figure we get,

*PC +CA =PA*

*DB +PD =PB*

Therefore,

Perimeter of is *PA + PB*

It is given that PA = 14 cm. again from the same property of tangents which says that the length of two tangents drawn to a circle from the same external point will be equal, we have,

*PA = PB*

Therefore,

Perimeter of = 2*PA*

Perimeter of = 2 × 14

Perimeter of = 28

Thus perimeter of is 28 cm.