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