Chords AB and CD intersect at point F so that AF = 4cm, BF = 16cm, CF = DF What is the length of the segment CD?

univerkov | May 20, 2021 | education

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

CF * DF = AF * BF.

Let the length of the segment DF = X cm, then СF = X cm, since DF = CF.

X * X = 4 * 16.

X ^ 2 = 64.

X = 8 cm.

CF = DF = 8 cm.

CD = 8 + 8 = 16 cm.

Answer: The length of the CD segment is 16 cm.

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