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**Assignment #23: Circles (1) **

**Due: 1/5 or 1/6 **

3.

**Directions: Please show your work for each of the following problems. Be sure to share care in setting up each scenario, given the following information. Double-check your set-up before attempting to work through each exercise. **

1.

Explain why this is a true theorem. *If two chords are equal then they have equal arcs and *

*central angles and vice versa. *

2.

Given arc AC = 20º, arc AB = 100º, AB = CD, and radius of circle = 10. a.

Find the measure in degrees of arc BD. b.

c.

Find the length of chord AB. (trig needed) Find the length of arc BD. A B C Given radius of circle = 10, PX = 21, OZ = 8 Find: PY = OP = X O Z Y P D

**Assignment #23: Circles (1) **

**Due: 1/5 or 1/6 **

4.

5.

6.

Find the radius. Chord AB has length 16. Find the radius.

*AB*

and

*CX*

The circles have radii of 5 and 11. are tangents. Find

*AX*

,

*XB*

, and

*XC*

. A X C B 9 9

*7*

4

*A B*

7.

One piece of a locomotive gear recovered in a train accident must be used to make a replacement. AB is carefully measured to be 81.9 cm. CD, the perpendicular bisector of AB, is measured to be 24.1 cm. Find the radius of the original gear. Maintain enough accuracy to be sure your final value is accurate to 0.1 cm.

*A C D B*

**Assignment #23: Circles (1) **

**Due: 1/5 or 1/6 **

8.

9.

Two circles have a common chord of length 48. The centers of the circles are 77 apart and the radius of the smaller is 40. Find the radius of the larger circle. Find the missing side of the circumscribed quadrilateral. 64 57 10.

These circles are mutually tangent and have radii 8 and 11. Find the length of common tangent AB. A 83 B