Special Segments in Circles

1. Special Segments in Circles Lesson 9.1B R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles CGT.5.G.4 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

2. Vocabulary Tangent line: A line that touches the circle at exactly one point. Tangent line is always perpendicular to the radius

3. Vocabulary Secant line: A line that intersects the circle at exactly two points.

4. d b a c The IIII Theorem If two chords or secant segments intersect inside a circle, then the products of the intersected pieces are congruent a · b = c · d

5. 8 x 3 6 Example Find the value of x.

6. 2 11 6 x Now You Try… Find the value of x.

7. Vocabulary External Secant Segment The piece of a secant that is between the circle and a point outside the circle. Tangent Segment The piece of a tangent line that is between the circle a point outside the circle.

8. IOIO Theorem If two secants are drawn from an exterior point to a circle, then the product of the measure of one secant’s external segment with the sum of the internal and external segments is equal to the product of the measure of the other secant’s external segment with the sum of the internal and external segments.

9. b d a c b(a+b) = d(c+d)

10. x 18 6 8 Example Find the value of x.

11. 9 x 3 4 Now You Try… Find the value of x.

12. IOO Theorem If a secant and tangent are drawn from an exterior point to a circle, then the square of the measure of the tangent segment is equal to the product of the measure of the secant’s external segment with the sum of the internal and external segments

13. b a c a2 = b(b+c)

14. 12 8 x + 4 Example Find the value of x.

15. 12 9 x Now You Try… Find the value of x.