# Section 10-1 The Circle A PowerPoint by Kathleen Calcerano.

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Section 10-1 The Circle A PowerPoint by Kathleen Calcerano

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

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

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

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

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

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

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

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

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

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.