AB.
14. 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. Prove PA. AQ = RA .AS.
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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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