#13 Circles

Basic Circle Terminology and Formulas

• The formula for the circumference of a circle is 2πr
• The formula for the area of a circle is πr^2

The Circle Equation

Arcs and Sectors

• Arc length; x/360 x 2πr
• Sector area; x/360 x πr^2

Radians and Degrees (Conversion)

Triangles With Radii Sides

Distances on The XY Plane

There’s two ways to find distance between two points. First you can connect the two by creating a right triangle and using the Pythagorean theorem to find the hypotenuse/distance. Another way is obviously the distance formula

• d=√(x2-x1)^2+(y2-y1)

Midpoint Formula

• (x1+x2/2, y1+y2/2)

General Form of Circle Equation

Sometimes, College Board will give you circle equations in general form, and the only way to solve them is by “completing the square”. If it’s the other way around and you’re given the normal circle equation and you need to convert it into general form, all you need to do is FOIL.

• Ex. x^2-6x+3=10
  • Rearrange the equation into ax^2+bx=c form; x^6-gx=7
  • Add (b/2)^2 to both sides of the equation; b=-6 > (-6/2)^2 > (-3)^2 > 9
  • x^2-6x+9=7+9
  • Factor the x^2+bx+(b/2)^2 into the perfect square; (x-3)^2=16 > √(x-3)^2=√16 > x-3= +/- 4
  • x-3=4 > x=7 and x-3=-4 > x=-1

Inscribed Angles

• Central angle (B) = intercepted arc (the
• The Inscribed Angle (D) is half the measure of the central angle