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Section 10.1 Circles

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10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point.

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10.1 Notes There are points ON, IN, and OUTSIDE the circle. The points in the circle make up the INTERIOR of the circle.

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10.1 Notes There are points ON, IN, and OUTSIDE the circle. The points outside the circle are EXTERIOR POINTS.

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10.1 Notes A chord of a circle is a segment with both endpoints ON the circle. is a chord.

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10.1 Notes A diameter of a circle is a chord that passes through the center. is a diameter.

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10.1 Notes A radius of a circle is a segment with one endpoint at the center of the circle and the other endpoint on the circle. and are radii.

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10.1 Notes All radii are congruent since all points on the circle are equidistant from the center of the circle.

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10.1 Notes Can you see a relationship between the radius and diameter of a circle?

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10.1 Notes A diameter of a circle is equal to two radii of the circle. A radius of a circle is equal to half of a diameter of the circle.

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10.1 Notes Finding diameter given radius: r=6 r=1.7cm d=12 d=3.4cm

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10.1 Notes Finding diameter given radius: r=4ft d=8ft r= m d= m

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10.1 Notes Find diameter given radius: 1. 2. r=12m 3. r=7ft

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10.1 Notes Finding radius given diameter: 1.2.

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10.1 Notes Finding radius given diameter: 1.

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10.1 Notes Finding radius given diameter: 2.

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10.1 Notes Finding radius given diameter: d= cm r= cm d=9m r=4.5m

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10.1 Notes Find radius given diameter: 1. AB=30in PC=? PC=15in 2. d=42ft r=21ft 3. d=10cm r=5cm

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10.1 Notes Tangent: a line which intersects a circle at exactly one point. Point of tangency: the point where the tangent intersects the circle.

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10.1 Notes A common tangent is a line that is tangent to two circles. A common tangent can either be a common external tangent or a common internal tangent.

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10.1 Notes common external tangent

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10.1 Notes common internal tangent

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10.1 Notes common external tangent

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10.1 Notes common internal tangent

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10.1 Notes Secant: a line that intersects a circle at two points.

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10.1 Terms to know exterior points-points that lie outside a circle. interior points-points that lie inside a circle. chord- a segment whose endpoints are on the circle. diameter-a chord that passes through the center of a circle. radius-a segment with one endpoint at the center of the circle and the other endpoint on the circle. tangent-a line which intersects a circle at exactly one point. point of tangency-the point where the tangent intersects the circle. common external tangent-a line that is tangent to two circles and DOES NOT intersect the segment connecting the two centers. common internal tangent-a line tangent to two circles that DOES intersect the segment connecting the two centers. secant-a line that intersects a circle at two points.

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