Mathematics
In the figure (ii) given below, two circles with centres C, C' intersect at A, B and the point C lies on the circle with C'. PQ is a tangent to the circle with centre C' at A. Prove that AC bisects ∠PAB.
Circles
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Answer
In △ACB,
AC = BC (Radius of the same circle)
∴ ∠BAC = ∠ABC ….(i)
PAQ is tangent and AC is the chord of the circle.
∠PAC = ∠ABC (∵ angles in alternate segment are equal) ….(i)
From (i) and (ii)
∠BAC = ∠PAC
Hence, proved that AC bisects ∠PAB.
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