Question

A
D
E
C
B
Andre drew a circle with chords AB
and CD
intersecting at point E
. He measures segments CE=12
, BE=9
, and DE=15
. What is the measurement of segment AE
?

(1 point)
AE=

Answer 1

To solve for segment AE, we can apply the intersecting chords theorem. This theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

In the given scenario, we have:
- \( CE = 12 \)
- \( BE = 9 \)
- \( DE = 15 \)
- \( AE \) is the unknown segment we want to find.

According to the theorem:
\[
AE \cdot BE = CE \cdot DE
\]

Substituting the known values into the equation:
\[
AE \cdot 9 = 12 \cdot 15
\]

Calculating \( 12 \cdot 15 \):
\[
12 \cdot 15 = 180
\]

Now we can replace that in the equation:
\[
AE \cdot 9 = 180
\]

To isolate \( AE \), divide both sides by 9:
\[
AE = \frac{180}{9} = 20
\]

Thus, the measurement of segment \( AE \) is:
\[
\boxed{20}
\]