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Section 10.1 Circles. 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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Presentation on theme: "Section 10.1 Circles. 10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point."— Presentation transcript:

1 Section 10.1 Circles

2 10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point.

3 10.1 Notes There are points ON, IN, and OUTSIDE the circle. The points in the circle make up the INTERIOR of the circle.

4 10.1 Notes There are points ON, IN, and OUTSIDE the circle. The points outside the circle are EXTERIOR POINTS.

5 10.1 Notes A chord of a circle is a segment with both endpoints ON the circle. is a chord.

6 10.1 Notes A diameter of a circle is a chord that passes through the center. is a diameter.

7 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.

8 10.1 Notes All radii are congruent since all points on the circle are equidistant from the center of the circle.

9 10.1 Notes Can you see a relationship between the radius and diameter of a circle?

10 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.

11 10.1 Notes Finding diameter given radius: r=6 r=1.7cm d=12 d=3.4cm

12 10.1 Notes Finding diameter given radius: r=4ft d=8ft r= m d= m

13 10.1 Notes Find diameter given radius: r=12m 3. r=7ft

14 10.1 Notes Finding radius given diameter: 1.2.

15 10.1 Notes Finding radius given diameter: 1.

16 10.1 Notes Finding radius given diameter: 2.

17 10.1 Notes Finding radius given diameter: d= cm r= cm d=9m r=4.5m

18 10.1 Notes Find radius given diameter: 1. AB=30in PC=? PC=15in 2. d=42ft r=21ft 3. d=10cm r=5cm

19 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.

20 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.

21 10.1 Notes common external tangent

22 10.1 Notes common internal tangent

23 10.1 Notes common external tangent

24 10.1 Notes common internal tangent

25 10.1 Notes Secant: a line that intersects a circle at two points.

26 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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