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