Question

Two circles touch each other externally.

Prove that the tangents drawn to the two circles from any point on the common tangent are equal in length. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Let P be any point on the common tangent

We know that,

PC = PB (Tangents drawn from an external point to a circle are equal)

Also,

PC = PA (Tangents drawn from an external point to a circle are equal)

$\therefore$ from the above two equation

PA = PB

This is true for any point P on the common tangent.

Hence proved.