Question

If AB and CD are common tangents to two circles of unequal radii, then _________.

Answer 1

Here, AB and CD are common tangents to two circles of unequal radii and having centres O₁ and O₂.

AB and CD are produced to intersect at P.

Now, PB and PD are tangents drawn from external point P to circle with centre O₂.

∴ PB = PD .....(1) (Lengths of tangents drawn from an external point to a circle are equal)

Also, PA and PC are tangents drawn from external point P to circle with centre O₁.

∴ PA = PC .....(2) (Lengths of tangents drawn from an external point to a circle are equal)

Subtracting (1) from (2), we get

PA − PB = PC − PD

⇒ AB = CD

If AB and CD are common tangents to two circles of unequal radii, then __AB = CD__.