Area of Circles Chapter 7B

Circles and Arcs (7-6) Circle - the set of all points equidistant from a given point called the center We name a circle by its center (circle P) Radius - a segment that has one endpoint at the center and the other endpoint on the circle Diameter - a segment that contains the center of a circle and has both endpoints on the circle

Circles and Arcs (7-6) Congruent circles - circles with congruent radii Concentric circles - circles that lie in the same plane and have the same center Central angle - an angle whose vertex is the center of the circle

Circles and Arcs (7-6) Arc - a part of the perimeter of a circle The measure of an arc is the measure of its corresponding central angle. Semicircle - an arc that is half of a circle (name using three points) Minor arc - an arc that is smaller than a semicircle (two points) Major arc - an arc that is greater than a semicircle (three points)

Circles and Arcs (7-6) Name 3 major and 3 minor arcs: Find the measure of each arc.

Circles and Arcs (7-6) Adjacent arcs - arcs of the same circle that have exactly one point in common Arc Addition Postulate - The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Circles and Arcs (7-6) Circumference of a circle C = πd = 2πr

Circles and Arcs (7-6) Arc length is a fraction of a circle’s circumference Length of = • 2πr Congruent arcs - arcs that have the same measure and are in the same circle or congruent circles Add formula here

Circles and Arcs (7-6) Find the length of . Leave your answer in terms of . Add arc name here.

Areas of Circles and Sectors (7-7) Area of a circle A = πr2

Areas of Circles and Sectors (7-7) Sector of a circle - a region bounded by an arc of the circle and the two radii to the arc’s endpoints Area of a sector of a circle A = m 360 Fix formula here •πr2

Areas of Circles and Sectors (7-7) Find the area of sector EDF. Leave your answer in terms of π.

Areas of Circles and Sectors (7-7) Segment of a circle - a part of a circle bounded by an arc and the segment joining its endpoints Area of a segment of a circle: Area of sector - area of triangle

Areas of Circles and Sectors (7-7) Find the area of the shaded segment. Round your answer to the nearest tenth.

Areas of Circles and Sectors (7-7) Find the area of the shaded segment. Round your answer to the nearest tenth.

Geometric Probability (7-8)  

Geometric Probability (7-8) We can find probability using lengths and areas. Example with lengths: If I randomly put my finger on the top edge of the ruler, what is the probability that it lands between 6 and 10?

Geometric Probability (7-8) Example with areas: You try your luck at the coin toss game at the fair. If your toss is random and always hits the table, what is the probability it lands on one of the circles?

Geometric Probability (7-8) Another example with areas: How would you find the probability of hitting the receiver in this game if your toss always hits the square?