In a circle, AB and CD are two diameters which are perpendicular to each other. Find the length of chord AC.
Explanation:
Let the radius of the circle be 'r'.
∴ AB = CD = 2r
Let O be the center of the circle
AOC is a right triangle, where AO = OC = r
⇒ AC2 = AO2 + OC2
⇒ AC2 = r2 + r2 = 2r2
⇒ AC = √2 × r = √2 × AB/2
⇒ AC = AB/√2
Hence, option (b).
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