Question

AB and CD are common tangents to two circles of unequal radii. Prove that AB=CD
​

Answer 1

$\bf\huge\underline{Question}$

AB and CD are common tangents to two circles of unequal radii.

Prove that AB=CD

$\bf\huge\underline{Answer}$

Given, AB and CD are common tangents to two circles of unequal radii

To prove: AB = CD

Construction: Extend AB and CD, to intersect at P.

PA = PC

[Since, Length of tangents drawn from an external point to a circle is equal]

Also, PB = PD

Therefore, PA - PB = PC - PD

=> AB = CD