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in Mathematics by (53.1k points)

Let C1 and C2 be two circles with centres at points A and B, respectively, which intersect at point P. If θ is the angle of intersection of the circles, then

where r1 = AP and r2 = BP

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Suppose the tangent to circle C2 at point P meets the line AB at point T1 and the tangent to circle C1 at point P meets AB at point T2 (see Fig.). Therefore, PT2 is at right angles at AP and PT1 is at right angles to PB. It is given that  ΔT1T2 = θ. Now,

Therefore, using cosine rule to ΔPAB, we get

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