Sem. 1 Unit 6 Circles Without Coordinates

quadrilaterals and circles rule

the opposite angles of a quadrilateral inscribed in/circumscribed by a circle are supplementary

center of the circle

the point at the exact center of a circle. All points on a circle are the same distance from the center.

secant-secant theorem

the measure of a secant-secant angle is half of the difference between the measures of the two intercepted arcs

inscribed angle theorem

the measure of an inscribed angle is always half the measure of its intercepted arc

semicircle

a 180 degree arc; half of a circle

circle

a geometric figure consisting of all the points on a plane that are the same distance from a single point (called its center)

secant

a line or a line segment that intersects a circle in two points

diameter

a line segment that contains the center of the circle and has endpoints on the circle (chord that passes through the center). This term also refers to the length of this line segment; the diameter of a circle is twice the radius.

radius

a line segment that has one endpoint at the center of a circle and the other endpoint on the circle. Radius also means "the length of such a line segment." The radius of a circle is half its diameter. The plural of radius is radii.

tangent line

a line that intersects a circle at exactly one point (known as the point of tangency)

parallelograms and circles rule

a parallelogram inscribed in/circumscribed by a circle must be a rectangle

intercepted arc

a part of the circle (an arc) that is cut off from the rest of the circle's circumference by lines or segments intersecting the circle

arc

a part of the circumference of the circle

sector

a part of the interior of a circle bounded by an arc and the two radii that share the arc's endpoints

radian

a unit of angular measure determined by the condition: The central angle of one angle in a circle of radius 1 produces an arc length of 1. Measure of the central angle created by laying the radius along the circumference of the circle. There are 2pi radians in a full circle. The arc length, or circumference, of a full circle is 2*pi*r.

arc length

the length of an arc of a circle. It is calculated by multiplying the circumference of the circle by the fraction of the circle covered by the arc.

area of a circle formula

A = pi*r^2, r stands for "radius"

circumference formula

C = circumference r = radius C = 2*pi*r

inscribed figures rule (triangles, circles, polygons)

Triangle: inscribed in another figure if each vertex of the triangle touches that figure Circle: inscribed in a polygon if each side of the polygon is tangent to the circle Polygon: inscribed in another figure if each vertex of the polygon touches that figure

tangent-chord angle

an angle formed by a tangent and a chord that shares the point of tangency. The measure of a tangent-chord angle is half the measure of the intercepted arc inside the angle.

tangent-tangent angle

an angle formed by intersecting tangents. The measure of a tangent-tangent angle is half the difference of the measures of the intercepted arcs.

inscribed angle

an angle formed by two chords of a circle that share an endpoint

central angle

an angle that has its vertex at the center of a circle. It is said to intercept an arc that has endpoints where the angle and circle intersect.

major arc

an arc of a circle that is longer than half the circumference. The degree measure of a major arc is greater than 180 degrees. It lies outside the sides of a central angle.

minor arc

an arc of a circle that is shorter than half the circumference. The degree measure of a minor arc is less than 180 degrees. It lies between two radii of a central angle.

chord

any line segment whose endpoints are on the circle

circumcenter of a triangle

center of the only circle that can be circumscribed about the triangle. It is equidistant from the vertices of the triangle and is found at the intersection of the perpendicular bisectors of the triangle's sides. acute: inside right: on the hypotenuse obtuse: outside

inscribed

fit one object tightly inside another

circumscribed

fit tightly around

converse of the perpendicular radii rule

if a radius of a circle bisects a chord, then it is perpendicular to that chord

perpendicular radii rule

if a radius of a circle is perpendicular to a chord, then it bisects that chord

congruent chords rule

if two chords are the same distance from the center of a circle, then they are congruent

converse of congruent chords rule

if two chords in a circle are congruent, then they are the same distance from the center of the circle

intersecting chords theorem

intersecting chords form a pair of congruent vertical angles. The measure of each angle is half the sum of the measures of the intercepted arcs.

secant-secant angle

the angle formed by the intersection of two secants of the same circle. The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs.

area of a sector formula

the area of a sector is calculated by multiplying the area of the entire circle by the fraction covered by the sector

incenter of a triangle

the center of the only circle that can be inscribed in a triangle. It is equidistant from the sides of the triangle and is found at the intersection of the angle bisectors of the triangle.

circumference

the distance around a circle

point of tangency

the point at which a tangent line meets a curve. In a circle, the radius ending at the point of tangency is always perpendicular to the tangent line.

area

the space taken up by a two-dimensional figure or surface. Area is measured in square units, such as square inches, square centimeters, or square feet.

congruent chords and central angles rule

two chords are congruent only if their associated central angles are congruent

congruence of arcs rule

using central angles: two arcs of a circle are congruent only if their angles are congruent using congruent chords: two arcs of a circle are congruent only if their associated chords are congruent