1. Warm-Up: 1)simplify: (x – 1)² 2)Factor: 10r² – 35r 3) Factor: t ² + 12t + 36 4) Solve: 2x ² – 3x + 1 = x ² + 2x – 3 5) Find the radius of a circle with a 30 cm chord 20 cm away from the center of the circle.

2. 11.3: Inscribed Angles

3. Inscribed Angle Angle with its vertex on a circle and sides are chords of the circle  DEF is inscribed in  G  DEF intercepts DF DF is intercepted by  DEF

4. Inscribed Angle Theorem: The measure of an inscribed angle is one-half the measure of its intercepted arc. (or arc measure is twice inscribed angle measure) If DF=76°, then m  DEF=38°

5. Corollary 1: Two inscribed angles that intercept the same arc are congruent.  1 &  6 intercept WX, so  1   6 If m  1=47°, then WX=94°, and m  6=47°

6. Corollary 2: An angle inscribed in a semicircle is a right angle. BD is a diameter BCD is a semicircle, so  BAD = 90° BAD is a semicircle, so  BCD = 90°

7. Corollary 3: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Quadrilateral EFGH is inscribed in  N  E +  G = 180  F +  H = 180 If m  E=125°, If m  F=87°, then m  G=55° then m  H=93°

8. Theorem 11-10: The measure of an angle formed by a tangent and a chord is one-half the measure of the intercepted arc. W Z X Y V 115° 245°

9. 11.4: Angle Measures

10. Secant A line that intersects a circle in exactly 2 points Line AB is a secant to  N A B N

11. Theorem 11.11a: The measure of an angle formed by 2 lines intersecting inside of a circle is ½ the sum of the measures of its intercepted arcs. A B C D 164°22°

12. Theorem 11.11b: The measure of the angle formed by 2 lines intersecting outside of a circle is ½ the difference of the measures of the intercepted arcs. i) 2 secants: D B C A E 72° 15° x°

13. Theorem 11.11b: The measure of the angle formed by 2 lines intersecting outside of a circle is ½ the difference of the measures of the intercepted arcs. ii) secant-tangent: K L J M 146° 54° x°

14. Theorem 11.11b: The measure of the angle formed by 2 lines intersecting outside of a circle is ½ the difference of the measures of the intercepted arcs. iii) 2 tangents: S R T U 266° x°