Chapter 10 Definitions Chord Tangent Secant Central Angle Inscribed Angle Circumference Radius Diameter Arc Circle Success is dependent on effort. SophoclesSophocles Objective: Identify lines and line segments associated with circles. Solve problems involving circumference of a circle. Take a worksheet from the front create your own definitions for key parts of the circle. Make sure to include the additional terms not listed on the worksheet.

Spi.3.1 Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles). Check.2.2 Approximate pi from a table of values for the circumference and diameter of circles using various methods (e.g. line of best fit). Check.4.39 Identify lines and line segments associated with circles. Spi.4.8 Solve problems involving area, circumference, area of a sector, and/or arclength of a circle. Spi.4.13 Identify, analyze and/or use basic properties and theorems of circles to solve problems (including those relating right triangles and circles) Circles and Circumferences

Circle: Locus of all points in a plane equidistant from a point, the center Center: used to name the circle Radius Segment that goes from Center to Circle Diameter A chord that goes through the center Chord Segment with endpoints on circle C

Identify the Parts Name the Circle – E, circle E Name the radii – AE, BE, CE, DE Name the Chords – AD, BD, AB, AC Name the Diameters – AC, BD

Find the Radius and Diameter DF and PG are Diameters If DF = 10, Find DA r = ½ D r = ½ (10)= 5 If PA = 7, find PG D = 2r PG = 2(7) = 14 If AG = 12, find LA All radii are congruent, LA = 12

Concentric Circles Share a center

Measures of Intersecting Circles Diameters of Circle A, B and C are 10 inches, 20 inches and 14 inches respectively. Find XB Find BY AX + XB = AB 5 + XB = 10 XB = BY + YC = BC BY + 7 = 10 BY = 3 53

Measures of Intersecting Circles Diameters of Circle X, Y and Z are 22 inches, 16 inches and 10 inches respectively. Find EZ Find XF EZ =EF+FZ EZ=22+5=27 XF = 11

Key Formulas of Circles Find C if r = 7 Find C if d=12.5 Find d and r if C = 136.9

Using other figures to find Circumference a 2 + b 2 = c = c = c 2 169= c 2 13= c

Find the circumference of K 45,45, 90 Triangle r = 3 C= 6 

Circles, Circumferences Summary Practice Assignment Page 687, even* Honors Page 688, 26 – 42, 44 even*

Honors Page 688, 26 – 42, 44 even* 42. Congruent ft