Geometry Lesson 10.1.notebook April 29, 2015
Circles and Circumference
Circle the locus or set of all points in a plane equidistant from a given point called the center of the circle. or Circle C
Radius (plural radii) a segment with one endpoint at the center and the other on the circle.
Chord a segment with endpoints on the circle.
Diameter a chord that passes through the center of the circle and is made up of collinear radii.
Example: Name the circle, a radius, a chord, and a diameter of the circle.
1 Geometry Lesson 10.1.notebook April 29, 2015
Radius and Diameter Relationships
If a circle has a radius r and diameter d, the following relationships are true.
Radius Formula Diameter Formula
a. If QV = 8 inches, what is the diameter of Circle Q?
b. If TU = 14 feet, what is the radius of Circle Q?
Two circles are congruent if and only if they have congruent radii.
Concentric Circles are coplanar circles that have the same center.
2 Geometry Lesson 10.1.notebook April 29, 2015
The diameter of is 30 units, the diameter of is 20 units, and DS = 9. Find CD. Find RC.
Circumference the distance around the circle. The ratio of the circumference to the diameter C/d is an irrational number called pi
Find the circumference of a circle with a radius of 79 ft.
3 Geometry Lesson 10.1.notebook April 29, 2015
Find the diameter and radius of a circle to the nearest hundredth if the circumference is 106.4 millimeters.
If d = 33.87, then the radius is
a. Find the diameter and radius of a circle to the nearest hundredth if the circumference of the circle is 77.8 cm.
A polygon is inscribed in a circle if all its vertices lie on the circle.
A circle is circumscribed about a polygon if it contains all the vertices of the polygon. • Quadrilateral LMNP is inscribed in • Circle K is circumscribed about quadrilateral LMNP.
4 Geometry Lesson 10.1.notebook April 29, 2015
Find the exact circumference of if a square with side length 9 inches is inscribed in
Since the diagonal cuts the square into 2 triangles, the length of the diagonal is . Since the diagonal is also the diameter of Circle J, the circumference is C = πd or C = 9π√2 in.
Try: Find the exact circumference of the circle with an inscribed right triangle with legs 7 m and 3 m long.
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