Inside a circle of radius 15 at a distance of 7 units. point M is marked from the center, through which the chord AB = 27 is drawn.

| January 10, 2021 | education

Inside a circle of radius 15 at a distance of 7 units. point M is marked from the center, through which the chord AB = 27 is drawn. Find the product of the lengths of the segments into which the point M divides the chord AB.

Draw a chord EC through the center of the circle and point M. The length of the segment EM, the chord EC is equal to: EM = (R + OM) = (15 + 7) = 22 cm, the length of the segment CM, chord EC is equal to: CM = (R – OM) = (15 – 7) = 8 cm.
By the property of intersecting chords, the product of the lengths of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.
AM * BM = CM * EM = 22 * 8 = 176.
Answer: The product of the lengths of the segments of the chord AB is equal to 176 cm.



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