http://www.ck12.org Chapter 9. Circles
9.9 Segments from Chords
Here you’ll learn how to solve for missing segments from chords in circles.
What if Ishmael wanted to know the diameter of a CD from his car? He found a broken piece of one in his car and
took some measurements. He places a ruler across two points on the rim, and the length of the chord is 9.5 cm. The
distance from the midpoint of this chord to the nearest point on the rim is 1.75 cm. Find the diameter of the CD.
After completing this Concept, you’ll be able to use your knowledge of chords to solve this problem.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter9SegmentsfromChordsA
MEDIA
Click image to the left for more content.Brightstorm:Secants
Guidance
When two chords intersect inside a circle, the two triangles they create are similar, making the sides of each triangle
in proportion with each other. If we removeADandBCthe ratios betweenAE,EC,DE, andEBwill still be the
same.
Intersecting Chords Theorem:If two chords intersect inside a circle so that one is divided into segments of length
aandband the other into segments of lengthcanddthenab=cd. In other words, the product of the segments of
one chord is equal to the product of segments of the second chord.
Example A
Findxin the diagram below.
Use the ratio from the Intersecting Chords Theorem. The product of the segments of one chord is equal to the
product of the segments of the other.