http://www.ck12.org Chapter 9. Circles
Concept Problem Revisited
Think of this as two chords intersecting each other. If we were to extend the 1.75 cm segment, it would be a diameter.
So, if we findxin the diagram below and add it to 1.75 cm, we would find the diameter.
4. 25 · 4. 25 = 1. 75 ·x
18. 0625 = 1. 75 x
x≈ 10. 3 cm,making the diameter10. 3 + 1. 75 ≈ 12 cm,which is the
actual diameter of a CD.Vocabulary
Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the circle. Achordis a line segment whose endpoints are on a circle. Adiameteris
a chord that passes through the center of the circle. The length of a diameter is two times the length of a radius. A
central angleis the angle formed by two radii and whose vertex is at the center of the circle. Aninscribed angle
is an angle with its vertex on the circle and whose sides are chords. Theintercepted arcis the arc that is inside the
inscribed angle and whose endpoints are on the angle.
Guided Practice
Findxin each diagram below. Simplify any radicals.
Answers
For all problems, use the Intersecting Chords Theorem.
15 · 4 = 5 ·x
60 = 5 x
x= 122.
18 ·x= 9 · 3
18 x= 27
x= 1. 5