10.1 Use Properties of Tangents Hubarth Geometry

. A chord is a segment whose endpoints are on a circle Chord A diameter is a chord that passes through the center of a circle. Diameter A radius is a segment whose endpoints are the center of a circle and a point on the circle. Secant Radius A secant is a line that intersects a circle in two points A tangent is a line in the plane of a circle that intersects the circle in exactly one point. The point is called a point of tangency. . Tangent point of tangency

. . . . Ex 1 Identify special Segments and Lines Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter or a radius of circle C. B J K . C A D H . . . G F E Solution

Ex 2 Find Lengths in Circles in a Coordinate Plane Use the diagram to find the given lengths. a. Radius of A b. Diameter of A c. Radius of B d. Diameter of B a. The radius of A is 3 units. b. The diameter of A is 6 units. c. The radius of B is 2 units. d. The diameter of B is 4 units.

Ex 3 Draw Common Tangents Tell how many common tangents the circles have and draw them. a. b. c. a. 4 common tangents b. 3 common tangents c. 2 common tangents

Theorem 10.1 B l . C ⊙

Ex 4 Verify a Tangent to a Circle In the diagram, 𝑃𝑇 is a radius of P. Is 𝑆𝑇 tangent to P ? Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, ∆PST is a right triangle and 𝑆𝑇 ⊥ 𝑃𝑇 . So, 𝑆𝑇 is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, 𝑆𝑇 is tangent to P.

Ex 5 Find the Radius of a Circle In the diagram, B is a point of tangency. Find the radius r of C. You know from Theorem 10.1 that AB BC , so ∆ABC is a right triangle. You can use the Pythagorean Theorem. AC2 = BC2 + AB2 (r + 50)2 = r2 + 802 r2 + 100r + 2500 = r2 + 6400 100r = 3900 r = 39 ft .

Theorem 10.2 R . P S T

Ex 6 Use Properties of Tangent RS is tangent to C at S and RT is tangent to C at T. Find the value of x. RS = RT 28 = 3x + 4 8 = x

Practice 1. Tell how many common tangents the circles have and draw them. a. b. 2. Is DE tangent to C? Yes 3. ST is tangent to Q. Find the value of r. r = 7 4. Find the value(s) of x. +3 = x