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 $\bar{A C}$ and $\bar{B D}$ intersect at point $E$ .

So, $A E \cdot E C = D E \cdot E B$ .

Example :

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

Substitute.

$\begin{array}{l} A E \cdot E C = D E \cdot E B \\ 7 \cdot 12 = D E \cdot 8 \\ \frac{7 \cdot 12}{8} = D E \\ 10.5 = D E \end{array}$

Therefore, $D E = 10.5$ units.

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