CK-12 Geometry Concepts

http://www.ck12.org Chapter 9. Circles

238857 · 251308 =x·(x+ 9849 )

60026674956 =x^2 + 9849 x

0 =x^2 + 9849 x− 60026674956

U se the Quadratic Formula x≈

− 9849 ±

√

98492 − 4 (− 60026674956 )

2

x≈ 240128. 4 miles

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. Atangentis a line that intersects a circle in exactly one
point. Thepoint of tangencyis the point where the tangent line touches the circle. Asecantis a line that intersects
a circle in two points.

Guided Practice

Findxin each diagram below. Simplify any radicals.

Answers:

Use the Two Secants Segments Theorem.

8 ( 8 +x) = 6 ( 6 + 18 )

64 + 8 x= 144

8 x= 80

x= 10

2.

4 ( 4 +x) = 3 ( 3 + 13 )

16 + 4 x= 48

4 x= 32

x= 8

3.