Circle
A set of points in a plane that are equidistant from a fixed center point.
Semi-Circle
Half of a circle; a semi-circle contains 180º, exactly half of the 360º in a circle.
Radius
A line segment that connects the center of a circle with any point on that circle’s circumference. Plural: radii.
Chord
A line segment that connects any two distinct points on a circle’s circumference.
Diameter
A line segment that passes through the center of a circle and whose endpoints lie on the circle.
Circumference of a Circle
The measure of the perimeter of a circle. The circumference of a circle can be found with this formula: C = 2πr, where C is the circumference, r is the radius, and π is a constant that equals approximately 3.14.
Central Angle
The angle created by any two radii.
Arc
A portion of a circle’s circumference (above), delineated by any two points on the circle’s circumference.
Length of an Arc
The proportion of the central angle (above) to 360 is the same as the proportion of the arc (above) to the circle’s circumference. For example, if the central angle is 60º, the proportion is 60/360 = 1/6. The arc, then, is 1/6 the length of the total circumference.
Area of a Circle
The area inside the circle. The area of a circle can be found with this formula: A = πr^2, where r is the radius of the circle and π is a constant that equals approximately 3.14.
Sector
A “wedge” of the circle, composed of two radii and the arc connecting those two radii.
Area of a Sector
The proportion of the central angle (above) to 360 is the same as the proportion of the area of the sector (above) to the area of the circle. For example, if the central angle is 60º, the proportion is 60/360 = 1/6. The sector, then, is 1/6 the area of the total area.
Inscribed Angle
Similar to a central angle (above), in that two of the points are where the radii intersect the circumference of the center. The inscribed angle, however, does not originate from the center of the circle; instead, it originates on the circumference of the circle. When an inscribed angle and a central angle intercept the same arc, then the inscribed angle is exactly half of the central angle.
Inscribed Triangle
A triangle drawn inside another shape, such that the vertices of the triangle coincide with points on the edge of the other shape. For a circle, the vertices of the triangle are also points on the circle’s circumference.
Right Triangle Inscribed in Circle
A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.
Cylinder
Composed of two circles on either end of a rolled up rectangle.
Surface Area of a Cylinder
Sum the areas of the three shapes. The two circles have area π * r^2, and the rectangle has area l * w. The length of the rectangle is equal to the circumference of the circle (2πr) and the width is equal to the height of the cylinder (h). Thus, the total surface area of the cylinder is 2(π * r^2) + 2πrh.
Volume of a Cylinder
V = π * r^2 * h, where V is the volume, r is the radius of the cylinder, h is the height of the cylinder, and π is a constant that equals approximately 3.14.
