It is one of the most important theorem to remember.

2. If two chords intersect inside a circle, then the
product of the lengths of the segment parts of one
chord is equal to the product of the lengths of the
segment parts of the other chord.
A B
D
C
E
Given:
Chords AC and BD intersect at E.
Prove:
AE CE = BE DE

3. Find:
a. x
b. mAS
M
S
A H
8 4
x 3

4. Find:
a. x
b. mAS
a. 8(3) = 4x
24 = 4x
24/4 = 4x/4
6 = x
M
S
A H
8 4
x 3
b. mAS = 4x
= 4(6)
= 24

5. Find:
a. x
b. mAE
c. mAD
A
B
C
D
E
x + 3 x
8 6

6. Find:
a. x b. mAE c. mAD
a. 6 (x+3) = 8x
6x + 18 = 8x
18 = 2x
9 = x
b. AE = x+3
= 9+3
= 12
A
B
C
D
E
x + 3 x
8
6
c. AD = AE + DE
= 12 + 6
= 18