1. HW Pg 625

2. Section 10.5 Segment Lengths in Circles
Chapter 10 Circles
Section 10.5
Segment Lengths in Circles
Find the lengths of segments of chords.
Find the lengths of segments of tangents and secants.

3. Example 1 Intersection of Two Chords Example 2 Solve Problems
Example 3 Intersection of Two Secants
Example 4 Intersection of a Secant and a Tangent
Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Key)
Lesson 7 Contents

4. Find the lengths of segments of chords.

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

6. Find x. Answer: 12.5 Find the lengths of segments of chords.
Example 7-1c

7. Find the lengths of segments of chords.
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.
Example 7-2a

8. Find the lengths of segments of chords.
Draw a model using a circle. Let x represent the unknown measure of the equal lengths of the chord which is the length of the organism. Use the products of the lengths of the intersecting chords to find the length of the organism. Note that
Example 7-2b

9. Take the positive square root of each side.
Find the lengths of segments of chords.
Segment products
Substitution
Simplify.
Take the positive square root of each side.
Answer: 0.66 mm
Example 7-2c

10. Find the lengths of segments of chords.
ARCHITECTURE Phil is installing a new window in an addition for a client’s home. The window is a rectangle with an arched top called an eyebrow. The diagram below shows the dimensions of the window. What is the radius of the circle containing the arc if the eyebrow portion of the window is not a semicircle?
Answer: 10 ft
Example 7-2d

11. Find the lengths of segments of tangents and secants.

12. Find the lengths of segments of tangents and secants.
Find x if EF 10, EH 8, and FG
Example 7-3a

13. Secant Segment Products
Find the lengths of segments of tangents and secants.
Secant Segment Products
Substitution
Distributive Property
Subtract 64 from each side.
Divide each side by 8.
Answer: 34.5
Example 7-3b

14. Find the lengths of segments of tangents and secants.
Find x if and
Answer: 26
Example 7-3c

15. Find the lengths of segments of tangents and secants.

16. Find x. Assume that segments that appear to be tangent are tangent.
Find the lengths of segments of tangents and secants.
Find x. Assume that segments that appear to be tangent are tangent.
Disregard the negative solution.
Answer: 8
Example 7-4a

17. Find x. Assume that segments that appear to be tangent are tangent.
Find the lengths of segments of tangents and secants.
Find x. Assume that segments that appear to be tangent are tangent.
Answer: 30
Example 7-4c

18. HW # 42 Pg Even