# In Fig. 9.14, common tangents AB and CD to two circles intersect at E. Prove that AB = CD

**Solution: **

Given, AB and CD are common tangents to two __circles__.

The __tangents__ intersect at E.

we have to prove that AB = CD

From the figure,

E is the external point

The tangents drawn through external point E are EA, EC, EB and ED.

We know that the tangents drawn through an external point to a circle are equal.

So, EA = EC ---------------- (1)

EB = ED ---------------------- (2)

Adding (1) and (2),

EA + EB = EC + ED

From the figure,

AB = EA + EB

CD = EC + ED

So, AB = CD

Therefore, it is proved that AB = CD.

**✦ Try This: **In the given figure, common tangents AB and CD to the two circles with centres O1 and O2 intersect at E. Prove that AB = CD.

Given, AB and CD are the common tangents drawn to both the circles.

AB and CD intersect at the point E

As the tangents drawn on circle from same point

EA = EC

EB = ED

So by adding both we get

EA + EB = EC + ED

So we get

AB = CD

Therefore, it is proved that AB = CD.

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 10

**NCERT Exemplar Class 10 Maths Exercise 9.3 Problem 7**

## In Fig. 9.14, common tangents AB and CD to two circles intersect at E. Prove that AB = CD

**Summary:**

In Fig. 9.14, common tangents AB and CD to two circles intersect at E. it is proven that AB = CD

**☛ Related Questions:**

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