Consider the following theorem.
If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.
O is the center of the circle.
A circle contains six labeled points and four line segments.
- The center of the circle is point O.
- Points A, B, C and D are on the circle. Point A is on the top middle, point B is on the bottom right, point C is slightly above the middle right, and point D is on the bottom left.
- A line segment connects points A and B.
- A line segment connects points C and D.
- A line segment connects points A and D.
- A line segment connects points C and B.
- Point E is the intersection of line segments A B and C D. Point E is to the right and slightly below point O.
Given:
Find:EC