The chords AB and CD of the circle meet at point M. Find: AM if CM = 18cm, MD = 3cm, MB = 9cm.

We use the property of intersecting chords. The product of the segments of one chord formed by the intersection point is equal to the product of the segments of the other chord.

AM * BM = DM * CM.

AM = DM * CM / BM = 3 * 18/9 = 6 cm.

Answer: The length of the segment AM is 6 cm.

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