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Section 10-1 The Circle A PowerPoint by Kathleen Calcerano

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What is a circle? A circle is : the set of all points in a plane that are a given distance (the radius) from a given point (the center) on the plane. A segment that joins the center to a point on the circle is also called a radius. The circle The center A radius

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In or Out? A point is outside [on the exterior of ] a circle if its distance from the center is greater that the radius. A point is inside [ on the interior of ] a circle if its distance from the center is less than the radius A point is on a circle if its distance from the center is equal to the radius. A B C

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Parts of a circle A DIAMETER of a circle is a chord that passes throuh the center of the circle A CHORD of a circle is a segment joining any two points on the circle

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More Definitions Two or more coplanar circles with the same center are Concentric Two circles are congruent if they have congruent radii The distance from the center of a circle to a chord is the measure of the perpendicular segment from the center to the chord

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Formulas Area of a circle: A= r Circumfrerence of a circle: A=2 r

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Theorems 74: If a radius is perpendicular to a chord, then it bisects the chord 75: If a radius bisects a chord (not diameter) then it is perpendicular to that chord 76: The perpendicular bisector of a chord passes through the center of the circle

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Examples A B C The distance from A to the center is 7. Find A 5 The distance from B to the center is 4. Find B The distance from C to the center is 5. Find C M N O P Q Which two line segments are perpendicular? NQ and MO Why? Thm 75: If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord

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Practice Find the area and circumference of the circle C= 19 A= 90.25 7 10 Find the area of the shaded region A= 51

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More Practice K L I J H Given: Radius of 30 KH = 18 Find:HI Find the area of the larger triangle Find the area of the circle Find the area of one of the smaller triangles Answers: Above- 24 Right- a. 196 b. 98 c. 196

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Works cited "Area of a Circle." Year 9 Interactive Maths- Second Edition. 2000. Mathsteacher.com PTY LTD.. 30 May 2008. Rhoad, Richard, George Milauskas and Robert Whipple. Geometry for Enjoyment and Challenge. New ed. New York, NY: McDougal, Littel, and Company, 1991.

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Circumference Around the circle. Arc Part of the circumference.

Circumference Around the circle. Arc Part of the circumference.

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