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Intersecting Chords Theorem

If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Math diagram

In the circle, the two chords A C ¯ and B D ¯ intersect at point E .

So, A E E C = D E E B .

Example :

In the circle shown, if A E = 7 , E C = 12 and B E = 8 , then find the length of D E .


A E E C = D E E B 7 12 = D E 8 7 12 8 = D E 10.5 = D E

Therefore, D E = 10.5 units.


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