In a circle of radius 14 cm, APB is a shorter arc and P is the midpoint of the arc. Let C be the midpoint of the chord AB and PC = 7 cm. What is the length of the chord AP?

Explanation

Let the center of the circle be O. OP = OA = 14 cm. Since PC = 7 cm, OC = OP - PC = 14 - 7 = 7 cm. In right \Delta OAC, AC = \sqrt{OA^2 - OC^2} = \sqrt{14^2 - 7^2}. In right \Delta ACP, AP = \sqrt{AC^2 + PC^2} = \sqrt{(14^2 - 7^2) + 7^2} = \sqrt{14^2} = 14 cm.

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