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Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?

Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles? Correct Answer 25

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The radius is the perpendicular bisector of the common chord.

The distance is 40 cm and if we join P and Q it will cut the common chord in half and the point of intersection assumed M.

A and B are centres of the two circles

APM and AQM will be two right triangles.

AP = AQ = radius

Using Pythagoras theorem AP2 = PM2 + AM2 = 400 + 152 = 400 + 225 = 625

∴ AP = 25

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