Math II Unit Nine
Terms in this set (43)
A ______ is the set of all points in a plane that are equidistant from a given point, called the center of the circle.
A ________ is the distance from the center of a circle to a point on the circle. It is also a segment whose endpoints are the center of the circle and a point on the circle.
Two circles that have the same radius are ___________ ____________.
The ___________ is the distance across a circle, through its center. It is also a chord that passes through the center of the circle.
What is your _______________?
A ________ is a segment whose endpoints are points on the circle.
A _________ is a line that intersects a circle in two points.
A _________ is a line that intersects a circle in exactly one point.
Coplanar circles are ____________ if they have the same center.
A ___________ ___________ is a line or segment that is tangent to two coplanar circles.
Interior of a circle
All points of the plane that are inside a circle are _________ ___ ___ ___________.
Exterior of a circle
All points of the plane that are outside a circle are __________ ____ ___ __________.
Point of Tangency
The point at which a tangent line intersects the circle to which it is tangent is the _________ ___ ______________.
If a line is tangent to a circle, then it is ______________ to the radius drawn to the point of tangency.
In a plane, if a line is perpendicular to a radius of a circle at its __________ on the circle, then the line is tangent to the circle.
If two segments from the ________ exterior point are tangent to a circle, then they are congruent.
A __________ _________ is an angle whose vertex is the center of a circle.
The ______ _____ is part of a circle that measures less than 180 degrees.
The _______ ___ is a part of the circle that measures between 180 and 360 degrees.
The ______________ is an arc whose endpoints are the endpoints of a diameter of the circle.
Measure of a minor arc
The _________ __ __ _________ ____ is equal to the measure of its central angle.
Measure of a major arc
The _________ __ ___ _________ ___ is the difference between 360 degrees and the measure of its associated minor arc.
___________ ____ are two arcs of the same circle or of congruent circles that have the same measure.
The measure of an arc formed by two __________ arcs is the sum of the measures of the two arcs.
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding _________ are congruent.
If a diameter of a circle is perpendicular to a chord, then the diameter __________ the chord and its arc.
If one chord is a _______________ __________ of another chord, then the first chord is a diameter.
In the same circle, or in congruent circles, two chords are congruent if and only if they are __________ from the center.
An __________ _________ is an angle whose vertex is on a circle and whose sides contain chords of the circle.
An _____________ _____ is the arc that lies in the interior of an inscribed angle and has endpoints on the angle.
An __________ ________ is a polygon whose vertices all lie on a circle.
A ____________________ __________ is a circle with an inscribed polygon.
If an angle is inscribed in a circle, then its measure is _______ the measure of its intercepted arc.
If two inscribed angles of a circle intercept the _______ arc, then the angles are congruent.
If a right triangle is inscribed in a circle, then the _____________ is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are _______________.
If a tangent and a chord intersect at a point ____ a circle, then the measure of each angle formed in one half the measure of its intercepted arc.
If two chords intersect in the interior of a circle, then the measure of each angle is on half the _____ of the measures of the arc intercepted by the angle and its vertical angle.
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is on half the _____________ of the measures of the intercepted arcs.
If two chords intersect in the interior of a circle, then the ________ of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
If two __________ __________ share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.
If a secant segment and a ___________ ________ share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment.
Standard equation of a circle
A circle with radius r and center (h,k) has this ____________ _________ ___ __ __________: ( x-h)^2 + (y-k)^2 = r^2.