Geometry Chapter 12 Circles

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Presentation transcript:

Geometry Chapter 12 Circles 12.2 Properties of Arcs Geometry Chapter 12 Circles

The Ferris wheel on the lower right has equally spaced seats, such that the central angle is 20. How many seats are on this ride? Why do you think it is important to have equally spaced seats on a Ferris wheel?

** 360° Circle – Set of all points equidistant from a given point Center ** 360° C ** Name the circle by its center. C D R Diameter – A segment that contains the center of a circle & has both endpts on the circle. Ex. TR Central Angle – Is an  whose vertex is the center of the circle. Ex. TCD

Finding measures of Central s B mBAE = = 40% of 360 = (.40) • 360 = 144 mCAD = 8% of 360 (.08)(360) = 28.8 mDAE = 27% of 360 = 97.2 25% 40% A C 8% 27% D E

More Circle terms Arc – Part of a Circle. * Measured in degrees ° Minor Arc – Smaller than a semicircle. (< 180°) * Named by 2 letters * Arc Measure = measure of central  * Ex: RS Major Arc – Greater than a semicircle. (> 180°) * Name by 3 letters * Order matters * Ex: RTS * Measure = Central  R S P T Semicircle – Half of a Circle. * Name by 3 letters * Ex: TRS = 180

Just like angles, you can add arcs. Adjacent Arcs – Are arcs of the same circle that have exactly one point in common. Ex: AB and BC B C A Arc Addition!! mBCA = mBC + mCA

Example: Finding the measures of Arcs 32° B mBC = mDB = mAD = mAB = mBOC = mBC + mCD mADC – mCD mABC – mBC 32 58 32 D O = 32 + 58 = 90 148° = 180 – 58 = 122 122° A = 180 – 32 = 148

List the congruent arcs in C below. AB and DE are diameters. Solution: ACD= ECB because they are vertical angles. DCB = ACE because they are also vertical angles.

Are the blue arcs congruent? Solution: Since the angles have the same central angle measure and in the same circle, the arcs are congruent. The two arcs have the same angle measure because they have the same central angle. But since they have different radii they are not congruent.

Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Find the measure of the arcs in circle A. EB is the diameter.

Find the measure of the arcs in circle O.