10.3 Arcs & Chords

1. 10.3 Arcs & Chords First & Last Name March 6, 2014 ______Block

2. The endpoints of a chord are also endpoints of an arc. • Theorem 10.2: In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

3. 1. Prove given ʘX, .

4. The chords of adjacent arcs can form a polygon. • A polygon is inscribed in a circle if each of its vertices lie on the circle. • A circle is circumscribed about a polygon if the circle contains all the vertices of the polygons.

5. 2. The main veins of a snowflake create six congruent central angles. Determine whether the hexagon containing the flake is regular (all the sides and angles are congruent).

6. 3. Determine the measure of each arc of the circle circumscribed about the traffic sign. a. b.

7. Theorem 10.3: In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.

8. 4. Circle O has a radius of 13 inches. Radius is perpendicular to chord which is 24 inches long. • If, find . • Find .

9. 5. In circle T, ZV=1, and TW=13. Find each measure. • XV • XY

10. Theorem 10.4: In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

11. 6. Chords and are equidistant from the center. If the radius of ʘG is 26, find AC and DE.

12. 7. In circle D, CF=8, DE=FD, and DC=10. Find each measure. • FB • BC • AB • ED

13. Exit Slip • Determine the measure of each arc of the circle circumscribed about the traffic sign. a. b. • Circle O has a radius of 10, AB=10, and . Find each measure. • AX • OX • In ʘP, PD=10, PQ=10, and QE=20. Find each measure. • AB • PE