2. Angles and Arcs October 2007

3. Warm-up Find the measure of BAD

4. Arcs A chord divides a circle into two arcs. The smaller arc is a minor arc, and the larger arc is a major arc.

5. Central Angle A central angle has its vertex at the centre of a circle, and two radii form the arms. Central angle AOC is described as subtended by the chord AC and by the arc AC.

6. Inscribed Angle An inscribed angle has its vertex on the circle, and two chords form the arms. Inscribed angle ABC is also described as subtended by the chord AC and by the arc AC.

7. The measure of an arc is the measure of the central angle subtended by the arc.

8. Inscribed angles subtended by the same arc, or by equal arcs, are congruent.

9. The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.

10. The angle inscribed in a semicircle is a right angle.

11. Use the properties of central angles, inscribed angles, triangles, and diameters to solve for x in each of the following:

13. Draw a circle Mark 4 points on the circumference of the circle Inscribe a quadrilateral in the circle Measure the angles What do you notice?

14. Cyclic Quadrilateral A quadrilateral inscribed in a circle Opposite angles in a cyclic quadrilateral are supplementary x y a b