Warm Up. 9.2 Introduction To Circles 1. Radius ___ 2. chord _ 3. diameter _ 4. secant _ 5. tangent _ 6. circle ___ Let’s talk about.

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Presentation transcript:

Warm Up

9.2 Introduction To Circles

1. Radius _____ 2. chord _____ 3. diameter _____ 4. secant _____ 5. tangent _____ 6. circle _____ Let’s talk about circles! We will construct a circle with some rope and tape!

Diameter Radius C = 2 r = d A = r 2 7in. Write the formula Plug in the numbers Give an answer with units Leave in terms of unless otherwise stated Find the circumference and area of this circle.

Find the circumference and area of the circle Leave in terms of r=7in.

Symbol for a circle Named with a letter P P C D 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. The red portion of the circle is called arc CD CDsymbol

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.

x-axis y-axis A(6,0) B (0,-6) Find the measure and the length of AB. Since the arc is one fourth of the circle, its measure is (360), or 90. 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

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. T C A Find the area of the sector CAT. Since we know that CT has a measure of 90, we can calculate the area of the sector CAT as a fraction of the area of A Area of sector CAT = (area of A) = ( 6 2 ) = 9 u 2 or u 2

B C A 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 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. * Measure of the intercepted arc is double the measure of the inscribed angle

eometry/circle/inscribed- angle.html

Reflection review: y x H (4,9) T(10,2) Reflect point H over the y-axis to H’. Then find the slope of HT and of TH’