Question

Prove that If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square on the length of the tangent from the point of contact to the point of intersection.

Answer 1

Data:

A chord AB and a tangent TP at a point T on the circle intersect at P.

To Prove:

AP x BP = PT²

Construction:

Join AT and BT.

Proof: