1. 5-Minute Check on Lesson 10-6 Transparency 10-7 Click the mouse button or press the Space Bar to display the answers. Find x. Assume that any segment that appears to be tangent is tangent. 1. 2. 3. 4. 5. What is the measure of  XYZ if YZ is tangent to the circle? Standardized Test Practice: ACBD 55110125 250 C 70° 125° 110°35°

2. Lesson 10-7 Segments inside and outside the Circle

3. Objectives Find measures of segments that intersect in the interior of a circle Find measures of segments that intersect in the exterior of a circle

4. Circles – Special Segments J J K K L M M N J K T M LJ · JM = NJ · JKJK · JM = JL · JNJT · JT = JK · JM Two Chords Inside a Circle Two Secants From Outside Point Secant & Tangent From Outside Point L N Inside the circle, it’s the pieces of the chords multiplied together Outside the circle, it’s the pieces outside multiplied by the whole length

5. Example 7-1a Find x. Theorem 10.15 Multiply. Divide each side by 8. Answer: 13.5

6. Example 7-1c Find x. Answer: 12.5

7. Example 7-2a BIOLOGY Biologists often examine organisms under microscopes. The circle represents the field of view under the microscope with a diameter of 2 mm. Determine the length of the organism if it is located 0.25 mm from the bottom of the field of view. Round to the nearest hundredth. Answer: 0.66 mm B H F x x E G Draw a model using a circle. Let x represent the unknown measure of the equal lengths of the chord BF, which is the length of the organism. Use the products of the lengths of the intersecting chords to find the length of the organism.

8. Example 7-3a Find x if EF 10, EH 8, and FG 24. Secant Segment Products Substitution Distributive Property Subtract 64 from each side. Divide each side by 8. Answer: 34.5

9. Example 7-3c Answer: 26 Find x if and

10. Example 7-4a Answer: 8 Find x. Assume that segments that appear to be tangent are tangent. Disregard the negative solution.

11. Example 7-4c Find x. Assume that segments that appear to be tangent are tangent. Answer: 30

12. Summary & Homework Summary: –The measure of an angle formed by two secant lines is half the positive difference of its intercepted arcs –The measure of angle formed by a secant and tangent line is half its intercepted arc Homework: –pg 572 – 573; 8-10; 13-17; 22-24