Advanced Geometry Circles Lesson 1

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Presentation transcript:

Advanced Geometry Circles Lesson 1

Diameters, radii, and chords are all segments, Definition – the locus of all points in a plane equidistant from a given point A circle is named by its center point. Name: Diameters, radii, and chords are all segments, lines, or rays.

Examples: Identify each part of the circle below. Name the circle. Name a radius of the circle. Name a diameter of the circle Name a chord of the circle.

Examples: Circle R has diameters . and If ST = 18, find QM. 18 If RN = 2, find QM. 4 If PR = 11, find RT. 11

Example: The diameters of X, Y, and Z are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Find EZ.

Examples: Find each measure to the nearest hundredth. Find C if r = 13 inches. Find C if d = 6 millimeters. Find d and r to the nearest hundredth if C = 65.4 feet.

Examples: Find the exact circumference of K.

Find the exact circumference of P. Examples: Find the exact circumference of P. 9 ft 12 ft

Example: is a diameter of T. Find m RTS.

Central Angle Vertex is at the center Arc a piece of a circle

2 endpoints, 1 interior point, and Naming Arcs Minor Arc 2 endpoints and an arc symbol Major Arc 2 endpoints, 1 interior point, and an arc symbol

2 endpoints, 1 interior point, and Naming Arcs Semicircle 2 endpoints, 1 interior point, and an arc symbol

= 90 = 67 = 316 Examples: In P, and are diameters, m NPM = 46, bisects KPM, and . Find each measure. = 90 = 67 = 316

The table below shows the percent of each type Example: The table below shows the percent of each type of bicycle sold in the United States in 2001. Find the measure of the central angle representing each category. Type of Bicycle % Comfort 21 Mountain 37 Youth 26 Hybrid 9 Other 7 75.6º 133.2º 93.6º 32.4º 25.2º Describe the kind of arc associated with each category.