Numerical answer
Two circles, each of radius 5 cm, have their centres 6 cm apart. Find the length of their common chord (in cm).
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Answer: 8
The common chord is perpendicular to the line joining the centres and bisects it (since the circles have equal radii), so the perpendicular distance from either centre to the chord is 6/2 = 3 cm. Half the chord length = √(5²−3²) = √16 = 4 cm, so the full chord length = 2×4 = 8 cm.
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