1. Angles, Arcs, and Chords Advanced Geometry Circles Lesson 2

2. In a circle or in congruent circles, two minor arcs are congruent if their corresponding chords are congruent.

3. Inscribed & Circumscribed Quadrilateral ABCD is inscribed in X. X is circumscribed about quadrilateral ABCD. insidesurrounding ALL vertices of the polygon must lie on the circle.

4. Example: A circle is circumscribed about a regular pentagon. What is the measure of the arc between each pair of consecutive vertices?

5. In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.

6. is perpendicular to chord Example: Circle R has a radius of 16 centimeters. Radius, which is 22 cm long. If m = 110, find m. Find RS.

7. = 53, find m. is perpendicular to chord Example: Circle W has a radius of 10 centimeters. Radius, which is 16 cm long. If m Find JL.

8. In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. and are equidistant from the center. P is 15 and EF = 24, find PR and RH. Example: Chords If the radius of

9. Inscribed Angles & Intercepted Arcs If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc.

10. = 100. Find m 1, m 2, m 3, m 4, and m 5. Example: In O, m = 140, m

11. If two inscribed angles of a circle intercept congruent arcs or the same arc, then the angles are congruent.

12. Example: Find m ∠ 2 if m ∠ 2 = 5x – 6 and m ∠ 1 = 3x + 18.

13. Example: Triangles TVU and TSU are inscribed in P with. If the inscribed angle intercepts a semicircle, then the angle is a right angle. Find the measure of each numbered angle if m ∠ 2 = x + 9 and m ∠ 4 = 2x + 6.

14. S and m Example: Quadrilateral QRST is inscribed in If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. M. If m Q = 87 R = 102, T. find m and m

15. Example: Points M and N are on a circle so that m Suppose point L is randomly located on the same circle so that it does not coincide with M or N. What is the probability that m MLN = 40? Probability = 80.