1. An electric winch is used to pull a boat out of the water onto a trailer.  The winch winds the cable around a circular drum of diameter 5 inches.  Approximately how many times will the winch have to rotate in order to roll in 5 feet of cable?

2. Solve the system of equations
x=3, y=6

3. Use a compass to draw a circle and label the center C.
Warm-up
Use a compass to draw a circle and label the center C.
Draw an inscribed angle and label it ADB.
Draw
Measure ∠ADB and ∠ACB
Find the mXZ and compare it with m∠ADB.
Make a conjecture.

4. 10.3 Inscribed Angles Find measures of inscribed angles
Find measures of angles of inscribed polygons

5. An inscribed angle
An angle whose vertex is on a circle and whose sides contain chords of the circle. The arc that lies in the interior of an inscribed angle and has endpoints on the angle is called the intercepted arc of the angle.
inscribed
angle
intercepted
arc

6. Theorem 10.8 Measure of an Inscribed Angle
If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.
m∠ADB= ½ mAB

7. Theorem 10.9
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
∠C≅∠D

8. Find the measure of the arc or angle.
mADC mAC
3. m∠ABC
1800
1400
980

9. Find the m∠ABE, m∠ACE, and m∠ADE.
450, 450, 450

10. Theorem 10.10
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
∠B is a right angle iff

11. Theorem 10.11
A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary.
D, E, F, and G lie on some circle, ⨀C, iff m∠D+m∠F = 1800 and m∠E +m∠G = 1800.

12. Find the value of y and x.
x = 95, y = 100

13. mA∠=600, m∠B=1140, m∠C=1200, m∠D=660
In the diagram, ABCD is inscribed in ⨀P. Find the measure of each angle.