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. 5 Geometry Lesson 10.1.notebook April 29, 2015 P. 687 10­42 6.