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Geometry NAME: NOTES: Circles – Arcs & Central Angles PERIOD: DATE: Arcs & Central Angles of Circles A circle has a total of 360°… To understand angle relationships related to circles, the following terms are required: Central Angle An angle with its vertex at the center of the circle. Arc An unbroken part of a circle…any two points on a circle are the endpoints of the arc between them. Like an angle, arc’s have a corresponding degree measure. Minor arc An arc measuring less than 180°. Minor arcs are named using the arc’s endpoints with an arched “hat”… ex: AB The measure of a minor arc is equal to the measure of its central angle. (mAB) Major arc An arc measuring more than 180°, but less than 360°. Major arcs are named for the endpoints and a point between them… ex: ACB The measure of a major arc is equal to 360° minus the measure of its minor arc. Semicircle An arc whose endpoints are on a diameter of the circle. A semicircle also uses three letter notation. A semicircle measures 180°. Adjacent Arcs Two arcs in the same circle with exactly one point in common (an endpoint). Intercepted Arc The arc formed by intersecting an angle with a circle (the arc “cut off” by an angle) Use Circle Q to complete the following. B● 1) Name two central angles. 2) Name four (4) minor arcs. Q ● A 3) Name four (4) major arcs. 4) Name two (2) semicircles. ● D 5) Name two (2) minor arcs adjacent to AB. 6) Name two (2) major arcs adjacent to AB. 7) Name the arc intercepted by DQC. 8) If mAQD = 60°, then mAD = __________ and mABD = __________. 9) If mDBC = 220°, then mDC = __________ and mDQC = __________. C