The chords MK and PT intersect at point A. Find Am if AP = 2 dm, AT = 24 dm, AM: AK = 3: 4.

univerkov | September 17, 2021 | education

Let the length of the segment AK = X dm.

Then, by condition, AM / X = 3/4.

AM = 3 * X / 4 dm.

By the property of intersecting chords of a circle, 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.

AK * AM = AT * AР.

X * 3 * X / 4 = 24 * 2.

X2 = 48 * 4/3 = 64.

X = AK = 8 dm.

AM = 3 * 8/4 = 6 dm.

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

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