Question

Two circles intersect at A. Chords PAQ are drawn through A, each passing through the centre of one of the two circles and terminated by the circumference.Prove PA.AQ = RA.AS.

Answer 1

Given :   Two circles intersect at A. Chords PAQ and RAS are  drawn through A, each passing through the centre of  one of the two circles and terminated by the circum- ferences.

To Find : Prove PA. AQ = RA .AS.​

Solution:

PA is diameter as passes through center

=> ∠PRA = 90°

SA is Diameter as passes through center

=> ∠SQA = 90°

∠RAP = ∠QAS  Vertically opposite angles

ΔRAP  and ΔQAS

∠PRA = ∠SQA

∠RAP = ∠QAS

=> ΔRAP ≈ ΔQAS  ( AA criteria)

=> RA/QA = AP/AS

=> RA . AS = QA . AP

=> RA . AS = PA . AQ

=> PA. AQ = RA . AS

QED

Hence proved

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