The chords MK and PT meet at point A. Find AN if AP = 2cm, AT = 24cm, AM: KA = 3: 4.

univerkov | May 30, 2021 | education

Let the length AM = X cm, then, by condition, the length of the segment KA = 4 * X / 3cm.

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

KA * MA = AP * AT.

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

4 * X ^ 2 = 48 * 3

X ^ 2 = 48 * 3/4 = 36.

X = AM = 6 cm.

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

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