In a circle, two parallel chords on the same side of the diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

Let the perpendicular distance from the center to the 6 cm chord be x cm. Using the property of intersecting chords, half of the 6 cm chord is 3 cm, so by the Pythagorean theorem, the radius squared equals x squared plus 3 squared. Half of the 4 cm chord is 2 cm, and since the distance between the chords is 1 cm, its distance from the center is (x plus 1) cm, making the radius squared equal (x plus 1) squared plus 2 squared. Equating the two expressions gives x squared plus 9 equals x squared plus 2x plus 1 plus 4, which simplifies to 2x equals 4, so x is 2 cm. The radius squared is 2 squared plus 3 squared, which is 13, making the radius the square root of 13 cm.

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