EXAMPLE 1 Identify special segments and lines Tell

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EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. a. AC SOLUTION a. AC is a radius because C is the center and A is a point on the circle.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. b. AB SOLUTION b. AB is a diameter because it is a chord that contains the center C.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. c. DE SOLUTION c. DE is a tangent ray because it is contained in a line that intersects the circle at only one point.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. d. AE SOLUTION d. AE is a secant because it is a line that intersects the circle in two points.

GUIDED PRACTICE for Example 1 1. In Example 1, what word best describes AG

GUIDED PRACTICE for Example 1 1. In Example 1, what word best describes AG ? CB ? SOLUTION AG Is a chord because it is a segment whose endpoints are on the circle. CB is a radius because C is the center and B is a point on the circle.

GUIDED PRACTICE 2. for Example 1 In Example 1, name a tangent and a

GUIDED PRACTICE 2. for Example 1 In Example 1, name a tangent and a tangent segment. SOLUTION A tangent is DE A tangent segment is DB

EXAMPLE 2 Find lengths in circles in a coordinate plane Use the diagram to

EXAMPLE 2 Find lengths in circles in a coordinate plane Use the diagram to find the given lengths. a. Radius of b. c. Diameter of d. Diameter of Radius of A A B B SOLUTION a. The radius of A is 3 units. b. The diameter of c. The radius of d. The diameter of A is 6 units. B is 2 units. B is 4 units.

for Example 2 GUIDED PRACTICE 3. Use the diagram in Example 2 to find

for Example 2 GUIDED PRACTICE 3. Use the diagram in Example 2 to find the radius and diameter of C and D. SOLUTION a. The radius of C is 3 units. b. The diameter of c. The radius of d. The diameter of C is 6 units. D is 2 units. D is 4 units.

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and draw them. a. c. b. SOLUTION a. 4 common tangents b. 3 common tangents

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and draw them. c. SOLUTION c. 2 common tangents

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 4. SOLUTION 2 common tangents

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 5. SOLUTION 1 common tangent

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and

GUIDED PRACTICE for Example 3 Tell how many common tangents the circles have and draw them. 6. SOLUTION No common tangents

EXAMPLE 4 Verify a tangent to a circle In the diagram, PT is a

EXAMPLE 4 Verify a tangent to a circle In the diagram, PT is a radius of tangent to P ? P. Is ST SOLUTION 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.

EXAMPLE 5 Find the radius of a circle In the diagram, B is a

EXAMPLE 5 Find the radius of a circle In the diagram, B is a point of tangency. Find the radius r of C. SOLUTION You know from Theorem 10. 1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem. AC 2 = BC 2 + AB 2 Pythagorean Theorem (r + 50)2 = r 2 + 802 r 2 + 100 r + 2500 = r 2 + 6400 100 r = 3900 r = 39 ft. Substitute. Multiply. Subtract from each side. Divide each side by 100.

EXAMPLE 6 Find the radius of a circle RS is tangent to C at

EXAMPLE 6 Find the radius of a circle RS is tangent to C at S and RT is tangent to Find the value of x. C at T. SOLUTION RS = RT Tangent segments from the same point are 28 = 3 x + 4 Substitute. 8=x Solve for x.

GUIDED PRACTICE 7. Is DE tangent to for Examples 4, 5 and 6 C?

GUIDED PRACTICE 7. Is DE tangent to for Examples 4, 5 and 6 C? ANSWER Yes – The length of CE is 5 because the radius is 3 and the outside portion is 2. That makes ∆CDE a 3 -4 -5 Right Triangle. So DE and CD are

GUIDED PRACTICE 8. for Examples 4, 5 and 6 ST is tangent to Q.

GUIDED PRACTICE 8. for Examples 4, 5 and 6 ST is tangent to Q. Find the value of r. SOLUTION You know from Theorem 10. 1 that ST QS , so QST is a right triangle. You can use the Pythagorean Theorem.

GUIDED PRACTICE for Examples 4, 5 and 6 QT 2 = QS 2 +

GUIDED PRACTICE for Examples 4, 5 and 6 QT 2 = QS 2 + ST 2 Pythagorean Theorem (r + 18)2 = r 2 + 242 r 2 + 36 r + 324 = r 2 + 576 36 r = 252 r=7 Substitute. Multiply. Subtract from each side. Divide each side by 36.

GUIDED PRACTICE 9. for Examples 4, 5 and 6 Find the value(s) of x.

GUIDED PRACTICE 9. for Examples 4, 5 and 6 Find the value(s) of x. SOLUTION Tangent segments from the same point are 9 = x 2 Substitute. +3 = x Solve for x.

EXAMPLE 1 Identify special segments and lines TellEXAMPLE 1 Identify special segments and lines Tell
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