The chords AB and CD meet at point E. Find the length AB if CE = 8cm, DE = 9cm, and AE is twice the length of BE.

univerkov | March 25, 2021 | education

Let the length of the segment BE = X cm, then the length of the segment AE = 2 * X cm.

By the property of intersecting chords, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

BE * AE = CE * DE.

X * 2 * X = 8 * 9.

2 * X ^ 2 = 72.

X ^ 2 = 72/2 = 36.

X = BE = 6 cm.

AE = 2 * 6 = 12 cm.

Answer: The length of the segment BE is 6 cm, AE is 12 cm.

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