Circles

Definitions A circle is the set of all points in a plane that are the same distance from a fixed point called the center of the circle. A radius of a circle is a line segment extending from the center to the circle. A diameter is a line segment that joins two points on the circle and passes through the center. radius center diameter

Chords A chord is any line segment that joins two points on a circle. Therefore, a diameter is an example of a chord. It is the longest possible chord.

Chords and Radii Given a chord in a circle, any radius that bisects the chord (passes through its midpoint) is perpendicular to that chord. Also, if a radius is perpendicular to a chord, then it bisects the chord.

Pi (If you do not have a Pi button, use 3.14)

Circumference The length or “perimeter” of a circle Circumference is equal to Pi multiplied by the diameter. C = 2πr C = πD

Important formulae C = 2πr C = πD D = 2r A = πr2 Remember when finding the area, you must follow the order of operations (BEDMAS). R2 must be done first, because you do exponents before multiplication. If you are following the formula in order, it is really A = r2●π

Re-writing formulae Any of the formulae from the previous page can be re-written, depending on what you need to solve for. For example, C = πD can be re-written as: D = C If you are given the circumference π and need to find the diameter. (Circumference divided by π = Diameter)

Arc Length An arc is a portion of the circumference A central angle is the angle formed between the two radii that make up the two ends of the arc We will use a proportion to find the arc length (there is another way to do it, but you will learn it in Grade 11)

Angles Remember, a circle has 360º. Most protractors are semi-circles (half a circle), and they measure up to 180º. If you measure from one end of the diameter to the other, you will get 180º

Arc Length Use a proportion (remember those?) Central angle = arc length 360 circumference

Sectors The sector of a circle is the area that is bordered by an arc, and two radii. Think of a sector as a slice of pizza. The sector is what you cut out for the slice. The area shaded in green on the circle to the right is the sector.

Sector Area To find the area of a sector, set it up like a proportion (similar to finding arc length) Angle of sector = Area of sector 360 Total area of circle *Write down the example from the chalkboard*