- Arc whose endpoints are on or in the interior of a central angle. (Less than 180 degrees)- The measure of a minor arc is equal to the measure of it's central angle. (TWO LETTERS)
- Arc whose endpoints are on or in the exterior of a central angle. (Greater than 180 degrees)- The measure of a major arc is equal to 360 minus the measure of its central angle. (THREE LETTERS)
- Arc whose endpoints lie on a diameter. (Exactly 180 degrees)- The measure of a semicircle is equal to 180 degrees. (3 LETTERS)
An angle whose vertex is the center of a circle.
An unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.
Arcs of the same circle that intersect at exactly one point. (Arc PQ and Arc QR are adjacent arcs because they are sharing point "Q")
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Within a circle or congruent circles, ---- are two arcs that have the ----.
congruent arcs, same measure
In a circle or congruent circles...
1. Congruent central angles have congruent chords.2. Congruent chords have congruent arcs.3. Congruent arcs have congruent central angles.
In a circle, if a radius (or diameter) is perpendicular to a chord, then...
it bisects the chord and its arc.
In a circle, the perpendicular bisector of a chord...
is a radius (or diameter).
Interior of a Circle
Set of all points inside the circle.
Exterior of a Circle
The set of all points outside the circle.
A segment whose endpoints lie on a circle.
A line that intersects a circle at two points.
A line in the same plane as a circle that intersects it at exactly one point.
Point of Tangency
The point where the tangent and a circle intersect.
Two circles are congruent if and only if they have a congruent radii.
Coplanar circles with the same center.
Two coplanar circles that intersect at exactly one point.
A line that is tangent to two circles.
Common External Tangent
Look at Picture
Common Internal Tangent
Look at Picture (RED LINES)
If a line is tangent to a circle,
then it is perpendicular to the radius drawn to the point of tangency. (L is tangent to circle P--->PQ is perpendicular to L)
If a line is perpendicular to a radius of a circle at a point on the circle,
then the line is tangent to the circle.
If two segments are tangent to a circle from the same external point,
then the segments are congruent. (NA and NG are tangent to E--->NA is congruent toe NG)
Two circles with the same center are congruent.
A tangent to a circle intersects the circle at two points.
Tangent circles have the same center.
A tangent to a circle will form a rights angle with the radius that is drawn to the point of tangency.
A chord of a circle is a diameter.
In a circle, the perpendicular bisector of the chord must pass through the center of the circle. (T or F)
Any two points on a circle determine a minor/major arc. (T or F)
False, if the point are at a diameter, the circle will become two semicircles.
The set of all points in a plane equidistant from a given point. (center)
C=Pie(d) OR C=2Pie(r)
Equation of a Circle
(x-h)^2 + (y-k)^2=r^2Center= (h,k)radius= r "squared
Tangent to x axis
square the y and make radius
Tangent to y axis
square to x and make radius
Chord Chord Product Theorem
If two chords intersect int he interior of a circle, then the products of the lengths of the segments of the chords are equal. Ex: part(part)=part(part)
A segment of a secant with at least one endpoint of the circle.
External Secant Segment
A secant segment that lies in the exterior of the circle with one endpoint on the circle.
Secant-Secant Product Theorem
If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product of the other secant segment and its external segment.Ex: Whole(Out)=Whole(Out)
A segment of a tangent with one endpoint on the circle.
Secant-Tangent Product Theorem
If a secant and a tangent intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external equals the length of the tangent segment squared. Ex: Whole(Out)=Tangent^2
An angle whose vertex is on a circle and whose sides contain chords of the circle.
Consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them.
A chord or arc subtends an angle if its endpoints lie on the sides of the angle.
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc. Ex: angle=1/2(arc) OR 2(angle)=arc
If inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc,
then the angles are congruent.
An inscribed angle subtends a semicircle if and only if the angle is a
If a quadrilateral is inscribed in a circle,
then its opposite angles are supplementary.
Vertex is ON the Circle (Tangent and a Secant)
measure of angle=1/2(arc)
Vertex is INSIDE the Circle (Two Secants and chords Intersect)
measure of angle=1/2(Arc 1+Arc 2)
Vertex is OUTSIDE the Circle (Tangent and a secant, Two Tangents, or Two Secants)
measure of angle=1/2(Big Arc-Small Arc)
Unbroken part of a circle consisting of two points called the endpoints of all the points on the circle between them.
An angle whose vertex is the center of a circle. (Arc=Angle)