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If chords AB and CD of a circle intersect each other at a point P inside the circle, prove that : PA × PB = PC × PD.

Circles

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Answer

In △PAC and △PDB

∠APC = ∠DPB (Vertically opposite angles are equal)

∠CAP = ∠BDP (Angles in same segment are equal)

∴ △PAC ~ △PDB

We know that,

When two triangles are similar, the ratio of the lengths of their corresponding sides are proportional.

∴ PAPD=PCPB\dfrac{PA}{PD} = \dfrac{PC}{PB}

⇒ PA × PB = PC × PD.

If chords AB and CD of a circle intersect each other at a point P inside the circle, prove that : PA × PB = PC × PD. Mixed Practice, Concise Mathematics Solutions ICSE Class 10.

Hence, proved that PA × PB = PC × PD.

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