Section 10.1 Circles. 10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane...
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Transcript of Section 10.1 Circles. 10.1 Notes What is a CIRCLE? A CIRCLE is the set of all points in a plane...
![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/1.jpg)
Section 10.1 Circles
![Page 2: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/2.jpg)
10.1 Notes
What is a CIRCLE?
A CIRCLE is the set of all points in a plane equidistant from a given point.
A
![Page 3: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/3.jpg)
10.1 Notes
There are points ON, IN, and OUTSIDE the circle.
The points in the circle make up the INTERIOR of the circle.
A
![Page 4: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/4.jpg)
10.1 Notes
There are points ON, IN, and OUTSIDE the circle.
The points outside the circle are EXTERIOR POINTS.
A
![Page 5: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/5.jpg)
10.1 Notes
A chord of a circle is a segment with both endpoints ON the circle.
is a chord.A
B
C
BC
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10.1 Notes
A diameter of a circle is a chord that passes through the center.
is a diameter.
E
D
A
DE
![Page 7: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/7.jpg)
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.E
D
A
AEDA
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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.
![Page 9: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/9.jpg)
10.1 Notes
Can you see a relationship between the radius and diameter of a circle?
D
A
E
A
E
![Page 10: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/10.jpg)
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.
d r
r = 12d
d=2r
![Page 11: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/11.jpg)
10.1 Notes
Finding diameter given radius:
r=6
r=1.7cm
d=12
d=3.4cm
6d=2r
1.7 cm d=2r
![Page 12: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/12.jpg)
10.1 Notes
Finding diameter given radius:
r=4ft
d=8ft
r= m
d= m
d=2r
d=2r
d=24
2 3
3
![Page 13: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/13.jpg)
10.1 Notes
Find diameter given radius:
1.
2. r=12m
3. r=7ft
3.2 cm
d=6.4cm
d=24m
d=14ft
![Page 14: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/14.jpg)
10.1 Notes
Finding radius given diameter:
1. 2.
A P
B
C
AB = 18 ftPC = ?PB = ?
AB = 20mAP = ?PC = ?
![Page 15: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/15.jpg)
10.1 Notes
Finding radius given diameter:
1.
A P
B
C
AB = 20mAP = ?PC = ? r=
12d
d=AB=20m
r = 10m
![Page 16: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/16.jpg)
10.1 Notes
Finding radius given diameter:
2.
A P
B
C
AB = 18 ftPC = ?PB = ?
r = 9ft
r=12d
d=AB=18ft
![Page 17: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/17.jpg)
10.1 Notes
Finding radius given diameter:
d= cm
r= cm
d=9m
r=4.5m
r = 12d
r = 12d
4 8
2 8
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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
A
P
BC
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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.
point of tangency
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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
![Page 23: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/23.jpg)
10.1 Notes
common external tangent
![Page 24: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/24.jpg)
10.1 Notes
common internal tangent
![Page 25: 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.](https://reader035.fdocuments.in/reader035/viewer/2022070307/551b08815503465e7d8b5bad/html5/thumbnails/25.jpg)
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.