Chapter 10 - All Flashcards
Interior of a circle
Points inside of a circle.
Exterior of a circle
Points outside of a circle.
Chord
A segment whose endpoints are on the circle.
Diameter
A chord that passes through the cent of a circle.
Radius
A segment whose endpoints consist of the center of the circle and a point on the circle.
Tangent
If a line intersects a circle at exactly one point, then the line is a tangent of the circle.
Secant
If a line intersects a circle at two points, then the line is a secant of the circle.
Common tangent
A line that is tangent to two circles.
Common external tangent
A common tangent that does not intersect the segment that joins the centers of the circle.
Common internal tangent
A common tangent that intersects the segment that joins the centers of the circle.
Two circles can intersect in 4 different ways…
No points
One point
Two points
All points
Concentric circles
Circles that have the same center.
Congruent circles
Circles with congruent radii or diameters.
If a line is tangent to a circle
Then it is perpendicular 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 endpoints on the circle,
Then the line is tangent to a circle.
If two segments from the same exterior point are tangent to a circle,
Then they are congruent.
Inscribed circle
A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.
Circumscribed circle
A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.
Central angle
An angle whose vertex is the center of the circle.
Minor arc
Consists of the endpoints of the central angle and all points on the circle that are in the interior of the central angle.
Measure of a minor arc
Measure
Semicircle
An arc whose endpoints are the endpoints of the diameter.
Circle
A set of all points in a plane that are equidistant from a given point called the center.
Adjacent Arcs
Two arcs of the same circle are adjacent if they intersect at exactly one point.
Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.
Congruent arcs
In the same circle or congruent circles, two arcs are congruent if they have the same measure.
In the same circle or in congruent circles, two arcs are congruent if and only if
Their central angles are congruent.
In the same circle or in congruent circles, two arcs are congruent if and only if
Their corresponding chords are congruent.
If a diameter of a circle is perpendicular to a chord,
Then the diameter bisects the chord and its arcs.
If chord AB is a perpendicular Bisector of another chord,
Then AB is a diameter.
In the same circle or in congruent circles, two chords are congruent if and only if
They are equidistant from the center.
Inscribed angle
An angle whose sides are chords of a circle.
Intercepted arc
The arc that lies in the interior of an inscribed angle.
If an angle is inscribed in a circle,
Then it’s measure is half of the measure of its intercepted arc.
If two inscribed angles of a circle intercept the same arc,
Then the angles are congruent.
An angle that is inscribed in a circle is a right angle if and only if
It’s corresponding arc is a semicircle.
A quadrilateral can be inscribed in a circle if and only if
It’s opposite angles are supplementary.
If a tangent and a chord intersect at a point on a circle,
Then the measure of each angle formed is half the measure of its intercepted arc.
If two chords intersect in the interior of a circle,
Then the measure of each angle is half the sum of the measures of the arcs 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 is half the difference of the measures of the intersected arc.
The standard form of the equation of a circle
(X-h)^2 • (y-k)^2 = r^2
