1.  Moving on with Circles….. Going round and round again… Feb. 24, 2014 Geometry—Mr. Morrison 7 th period

2. 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-geometry- circles/circles/v/language-and-notation-of-the-circle https://www.khanacademy.org/math/geometry/cc-geometry- circles/circles/v/language-and-notation-of-the-circle

3. 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/basic- geometry/circum_area_circles/v/circles--radius--diameter-and- circumference https://www.khanacademy.org/math/geometry/basic- geometry/circum_area_circles/v/circles--radius--diameter-and- circumference

4. 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: https://www.khanacademy.org/math/geometry/cc-geometry- circles/circles/v/length-of-an-arc-that-subtends-a-central-angle https://www.khanacademy.org/math/geometry/cc-geometry- circles/circles/v/length-of-an-arc-that-subtends-a-central-angle

5. 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°

6. 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° 

7. 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.

8. 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.

9. 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.  Start the practice with worksheet…..