1. Lesson 10-4: Inscribed Angles

2. Lesson 10-4: Inscribed Angles
Inscribed Angle: An angle whose vertex lies on a circle and whose sides are chords of the circle (or one side tangent to the circle).
Examples: 3 1 2 4
No!
Yes!
No!
Yes!
Lesson 10-4: Inscribed Angles

3. Lesson 10-4: Inscribed Angles
Intercepted Arc
Intercepted Arc: An angle intercepts an arc if and only if each of the following conditions holds:
1. The endpoints of the arc lie on the angle.
2. All points of the arc, except the endpoints, are in the interior of the angle.
3. Each side of the angle contains an endpoint of the arc.
Lesson 10-4: Inscribed Angles

4. Lesson 10-4: Inscribed Angles
Inscribed Angle Theorem
The measure of an inscribed angle is equal to ½ the measure of the intercepted arc. Y
Inscribed Angle
110
55 Z
Intercepted Arc
An angle formed by a chord and a tangent can be considered an inscribed angle.
mAB 2
mABC =
or 2 (mABC ) = mAB
Lesson 10-4: Inscribed Angles

5. Lesson 10-4: Inscribed Angles
Examples: Find the value of x and y in the fig. y x 50 A B C E F y 40 x 50 A B C D E
Lesson 10-4: Inscribed Angles

6. Lesson 10-4: Inscribed Angles
An angle inscribed in a semicircle is a right angle. P
180
90 S R
Lesson 10-4: Inscribed Angles

7. Inscribed Quadrilaterals
If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.
mDAB + mDCB = 180 
mADC + mABC = 180 
Chapter 10-6: Interior and Exterior Angles