Question
Two circles of radius 13 cm and 15 cm intersect each
other at points A and B. If the length of the common chord is 12 cm, then what is the distance between their centres?Solution
Let O and R be the center of the circle and PQ be the length of the common chord. OP = 15, RP = 13 PS = 1/2 PQ (as perpendicular from the center of the circle to a chord bisects the chord) PS = 1/2 × 12 PS = 6 By applying Pythagoras theorem in PSO: OS2 = OP2-PS2 = 152 – 62 = 225-36 = 189  OS = √189  By applying Pythagoras' theorem in PSO': RS² = RP2-PS2 = 132 - 62 = 169-36 = 133 RS = √133 OR = OS + RS = √189 + √133 The distance between their centers = √189 + √133
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