Intersecting Chords Worksheet

Intersecting Chords

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

When two chords intersect inside a circle, they divide each other into segments. The Intersecting Chords Theorem states that the product of the segments of one chord is equal to the product of the segments of the other chord.

For example, if chords AB and CD intersect at point P, then AP × PB = CP × PD.

1. In the circle below, chords AB and CD intersect at P. If AP = 6, PB = 4, and CP = 3, what is the length of PD?

Calculation:

2. If two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the   chord.

3. Chords RS and TU intersect at V. If RV = 5, VS = 8, and TV = 10, what is the length of VU?

4. Chords EF and GH intersect at I. If EI = x, IF = 9, GI = 3, and IH = 12, find the value of x.

Solution:

5. The Intersecting Chords Theorem applies only when the chords are perpendicular.

6. Chords KL and MN intersect at O. If KO = 7, OL = 2, and MO = x, ON = 7, find the value of x.

Solution: