Chords AB and CD meet at point M. Find AB and CD if AM = 16cm, MB = 4cm, CM = MD.

univerkov | July 31, 2021 | education

By the property of intersecting chords, the product of the segments formed at the intersection of one chord is equal to the intersection of the segments of the other chord.

CM * DM = AM * BM

Let the length of the segment CM = X cm, then DМ = X cm, since DМ = CM.

X * X = 16 * 4 = 64.

X ^ 2 = 64.

X = CM = DM = 8 cm.

CD = CM + DM = 8 + 8 = 16 cm.

AB = AM + BM = 16 + 4 = 20 cm

Answer: The length of the segment CD is 16 cm, the length of the segment AB is 20 cm.

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