Circles

1. Circles Inscribed Angles

2. Inscribed Angles An angle whose vertex is on the circumference of the circle. Each side of an inscribed angle is a chord. A  FAB is an inscribed angle. Point A is the vertex. Segment FA is a chord. B Segment AB is a chord. F D

3. Inscribed Angles Arc FDB is an intercepted arc, made up by the inscribed angle. A Arc FDB is an intercepted arc. B F D

4. Measure of an inscribed angle The measure of Inscribed  = measure of Intercepted Arc ÷ 2.  YXZ is an inscribed angle. Arc YZ is an intercepted arc. Y Arc YZ = 86 m YXZ = arc YZ ÷ 2 X 43 m YXZ = 86 ÷ 2 86 m YXZ = 43 Z

5. Measure of an intercepted arc The measure of Intercepted arc = measure of inscribed  multiply by 2. Arc YZ is an intercepted arc.  YXZ is an inscribed angle. Y m YXZ = 73 Arc YZ = m YXZ * 2 X 73 Arc YZ = 73 * 2 146 Arc YZ = 146 Z

6. If two inscribed ’s intercepts the same arc, then the two ’s are .  ACB is an inscribed angle.  ADB is another inscribed angle.  ACB and  ADB intercepts arc AB. C D Arc AB = 112 56 56 m ACB = arc AB ÷ 2 m ACB = 112 ÷ 2 B m ACB = 56 A m ACB = m ADB = 56 112