Question

Two direct common tangents are drawn to two non-intersecting circles.prove that the segments between the points of contact are equal.

Answer 1

see attached file....hope it will help u

Answer 2

Proved below.

Step-by-step explanation:

Given:

Let AB and CD are common tangents to the circles with centres G and H

To prove:

The segments between the points of contact are equal.

that is, AB = CD

Construction:

BA and DC are extended , meet at point P.

Proof:

Since PB = PD        ( by tangent segment theorem which states that tangents drawn from an exterior point to a circle are equal in length )      [1]

Similarly,

PA = PC ( by tangent segment theorem which states that tangents drawn from an exterior point to a circle are equal in length )     (2)

Subtaracting Eq 2 fro Eq 1, we get

PB - PA = PD - PC

⇒ AB = CD

Hence Proved.