Transcript Document
Moving on with Circles….. Going round and round again… Feb. 25, 2014 Geometry—Mr. Morrison 7th period What we already know… The radius of a circle is the distance from the center of the circle to the outside edge. The diameter of a circle is longest distance across a circle. (The diameter cuts through the center of the circle. This is what makes it the longest distance.) Now take a look at this…. https://www.khanacademy.org/math/geometry/cc-geometrycircles/circles/v/language-and-notation-of-the-circle Area and Circumference…… The circumference of a circle is the perimeter -- the distance around the outer edge. Circumference = where r = the radius of the circle and pi = 3.141592... Area = where r = the radius of the circle and pi = 3.141592… A quick video refresher….. https://www.khanacademy.org/math/geometry/basicgeometry/circum_area_circles/v/circles--radius--diameter-andcircumference Circles—the inner workings…… A chord of a circle is a line segment that connects one point on the edge of the circle with another point on the circle. (The diameter is a chord -- it's just the longest chord!) An arc of a circle is a segment of the circumference of the circle. A quick video: http://www.khanacademy.org/math/geometry/cc-geometrycircles/circles/v/area-of-a-sector-given-a-central-angle Central Angle Measurements Central Angle: A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle. Central Angle = Intercepted Arc <AOB is a central angle. Its intercepted arc is the minor arc from A to B. m<AOB = 80° This should help—http://www.khanacademy.org/math/geometry/ccgeometry-circles/circles/v/finding-central-angle-measure-given-arc-length Inscribed Angle Measurement Inscribed Angle: An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords. Inscribed Angle =1/2 Intercepted Arc <ABC is an inscribed angle. Its intercepted arc is the minor arc from A to C. m<ABC = 50° Quick video: http://www.khanacademy.org/math/geometry/cc-geometry-circles/centralinscribed-circumscribed/v/inscribed-and-central-angles Special Situations for Inscribed Angles Special situations involving inscribed angles: An angle inscribed in a semi-circle is a right angle. In a circle, inscribed circles that intercept the same arc are congruent. Special situations for inscribed angles A quadrilateral inscribed in a circle is called a cyclic quadrilateral. The opposite angles in a cyclic quadrilateral are supplementary. Sectors A sector of a circle is a pie shaped portion of the area of the circle. Technically, the piece of pie is between two segments coming out of the center of the circle. Watch this…. http://www.khanacademy.org/math/geometry/cc-geometrycircles/circles/e/areas_of_circles_and_sectors Start the practice with worksheet…..