In the following figure, PQ is the tangent and PB is the scent. Prove

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

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

Answer»

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

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

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