Chords AB and CD intersect at point E. In this case, AE = 5, BE = 2, CE = 2.5. Calculate ED.

By hypothesis, chords AB and CD meet at point E, which divides them into segments AE = 5, BE = 2, CE = 2.5.

If two chords of a circle intersect at a point, then the product of segments of one chord is equal to the product of segments of the other chord.

In this way:

AE * BE = CE * DE.

Substitute the data on the value condition into this expression and find the length of the segment DE:

2.5 * DE = 5 * 2;

2.5 * DE = 10;

DE = 10 / 2.5 (according to the main property of the “cross to cross” proportion);

DE = 10: 25/10 = 10: 5/2 = 10 * 2/5 = (10 * 2) / 5 = 20/5 = 4.

Answer: DE = 4.