Question

In the following figure, PQ is the tangent and PB is the scent. Prove that PQ² = PA × PB

Answer 1

Considering the triangles PAQ and PQB.

∠APQ = ∠BPQ (Common angle)

∠PQA = ∠QBP (Angle between tangent and chord = the angle made by the chord on its . complimentary arc)

ΔPAQ ~ ΔPQB

[A.A Similarly]

∴ \(\frac{PA}{PQ}=\frac{AQ}{QB}=\frac{PQ}{PB}\)

[Ratio of the similar sides are equal]

∴ \(\frac{PA}{PQ}=\frac{PQ}{PB}\)

PQ² = PA × PB