Apply Other Angle Relationships in Circles

1. Apply Other Angle Relationships in Circles Lesson 10.5

2. Theorem 10.11 If a tangent and a chord intersect at a point on a circle, then B Angle 1 = ½(arcAB) Angle 2 = ½(arcBCA) C 1 2 A

3. Theorem 10.12Angles Inside the Circle Theorem Angle 1= ½(arcDC + arcAB) VERTICAL ANGLES Angle 2= ½(arcAD + arcBC) If two chords intersect inside a circle, then D A 1 2 C B

4. Theorem 10.13Angles Outside the Circle Theorem If a tangent and a secant, two tangents, or two secants intersect outside a circle, then B Angle1 = ½(arcBC-arcAC) A 1 C

5. Theorem 10.13Angles Outside the Circle Theorem Angle 2= ½(arcPQR-arcPR P 2 Q R

6. Theorem 10.13Angles Outside the Circle Theorem X Angle 3 = ½(arcXY- arcWZ) W 3 Z Y

7. Homework • 2-20even