The chords AB and CD of the circle intersect at point E. It is known that AE: EB = 1: 3, CD = 20, DE = 5. Find AB.

univerkov | May 6, 2021 | education

The length of the segment is CE = CD – DE = 20 – 5 = 15 cm.

Let the length of the segment AE = X cm, then BE = 3 * X cm.

By the property of intersecting chords, the product 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.

X * 3 * X = CE * DE.

3 * X ^ 2 = 15 * 5 = 75.

X ^ 2 = 25 cm.

X = AE = 5 cm.

BE = 3 * 5 = 15 cm.

AB = AE + BE = 5 + 15 = 20 cm.

Answer: The length of the chord AB is 20 cm.

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