question_answer

In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

Answer:

Construction: Extend AB and CD to meet at a point P

Now, PA and PC are tangents of circle with centre O

So                    \[PA=PC\]                                             ...(i)

PB and PD are tangent on circle with centre O?

So                    \[PB=PD\]                                             ...(ii)

On subtracting eq. (ii) from eq. (i)

\[PA-PR=PCPD\]

\[AB=CD\]                                Hence Proved