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Introduction to Circles

Introduction to Circles. Lesson 9.2. Find the circumference and area of this circle. Leave in terms of unless otherwise stated. Diameter. Radius. 7in. C = 2 r C = 2(7) C = 14 in. A = r 2 A = 7 2 A = 49 in 2. Symbol for a circle Named with a letter P. P.

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Introduction to Circles

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  1. Introduction to Circles Lesson 9.2

  2. Find the circumference and area of this circle. Leave in terms of unless otherwise stated Diameter Radius 7in. C = 2 r C = 2(7) C = 14 in. A = r2 A = 72 A = 49 in2

  3. Symbol for a circle Named with a letter P P An arc is made up of two points on a circle and all points of the circle needed to connect those two points by a single path. C D The red portion of the circle is called arc CD. CD symbol

  4. The measure of an arc is equivalent to the number of degrees it occupies. A complete circle has 360 degrees. The length of an arc is a fraction of a circle’s circumference, so it is expressed in linear units, such as feet, centimeters, or inches.

  5. y-axis Find the measure and the length of AB. A(6,0) x-axis Since the arc is one fourth of the circle, its measure is (360), or 90. B (0,-6) The arc’s length (l) can be expressed as a part of the circle’s circumference. l = C d = = 12 = 3 or 9.42 units

  6. (0,6) 90º A sector of a circle is a region bounded by two radii and an arc of the circle. The figure at the left shows sector CAT of A. (6,0) Find the area of the sector CAT. Since we know that CT has a measure of 90º, we can calculate the area of the sector CAT as a fraction of the area of A . • Area of sector CAT = (area of A) • = ( 62) • = 9 u2 or 28.27 u2

  7. A chord is a line segment joining two points on a circle. A diameter is a chord that passes through the center of the circle. An inscribed angle is an angle whose vertex is on a circle and whose sides are determined by two chords of the circle B A C AB and AC are chords, and <BAC is an inscribed angle. <BAC is said to intercept BC. (An intercepted arc is an arc whose endpoints are on the sides of an angle and whose other points all lie within the angle. Although <BAC intercepts only one arc, in Chapter 10 you will deal with some angles that intercept two arcs of a circle.)

  8. Reflection Review: y H’ (-4,9) H (4,9) T(10,2) x Reflect point H over the y-axis to H’. Find the slope of TH’. Slope = -7/14 = -1/2

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