Two circles of radii 20 cm and 16 cm intersect and the length of common chord is 24 cm. If d is the distance between their centres, then which one of the following is correct?

The line of centers perpendicularly bisects the common chord, creating two right triangles with a shared side of 12 cm. For the first circle, the distance from the center to the chord is found using the Pythagorean theorem: the square root of 20 squared minus 12 squared, which is 16 cm. For the second circle, the distance is the square root of 16 squared minus 12 squared, which equals sqrt(112) or approximately 10.58 cm. The total distance between the centers is the sum of these two distances, d = 16 + 10.58 = 26.58 cm. Therefore, 26 cm is less than d and d is less than 27 cm.

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