Chapter 10 Flashcards
Center
part of a circle that all points are equidistant from
Central Angle
angle with vertex in center of circle
chord
segment with endpoints on the circle
circle
set of all points equidistant from a given point
circumference
distance around the circle
diameter
chord that passes through center and is made of collinear radii
pi
the ration c/d, as an irrational number
radius
segment with endpoints at center and on the circle
Circle pairs
- 2 circles are congruent if they have congruent radii
2. all circles are similar
Concentric Circles
coplanar circles with same center
Inscribed polygon
polygon with vertices on the circle
Circumscribed polygon
polygon outside the circle
Arc
portion of the circle defined by 2 endpoints
Central Angle
angle with vertex in the center of the circle
Sum of Central Angles
360 degrees
Minor arc
connecting two endpoint that make up less than 180*
Major arc
connecting two endpoint s that make up more than 180*
Semicircle
arc with endpoints that lie on a diameter, or 180*
Congruent Arcs
arcs in same or congruent circles that have the same measure
In the same circle or in congruent circles, two minor arcs are congruent if an only if….
their central angles are congruent
Adjacent arc
arcs in a circle with exactly one point I common
Measure of arc formed by 2 adjacent arcs is the sum of the measure of
the two arcs
Arc Length
distance between endpoints along an arc, measured in degrees
in the same circle or congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are…
congruent
If a diameter or radius of a circle is perpendicular to a chord, then it…
bisects the chord and its arc
The perpendicular bisector of a chord is…
the diameter or radius of a circle
In the same circle or in congruent circles, 2 chords are congruent if and only if they are _______ from the _______
equidistant, center
Inscribed Angle
angle with a vertex on the circle and sides that contain chords of the circle
Intercepted Arc
endpoints on the sides of an inscribed angle and lies on the interior of the inscribed angle
If an angle is inscribed in a circle, the measure of the circle is ____ of the intercepted arc
1/2
If two inscribed angles of a circle intercept the same arc or congruent arcs, the angles are
congruent
An inscribed angle of a triangle intercepts a diameter or semicircle only if the angle is a _______ angle
right
If a quadrilateral is inscribed in a circle, it’s opposite angles are….
supplementary
Tangent to a Circle
a line that intersects the circle at exactly one point
Common Tangent
line, Ray, or segment that is tangent to 2 circles in the same plane
In a plane, a line is tangent to a circle if and only if it is _______ to a radius drawn to point of tangency
perpendicular
If two segments from the same exterior point are tangent to a circle, they are….
congruent
Secant
line that intersects a circle at 2 points
If an angle’s vertex is at the center of the circle, it’s measure is _____
same as the measure of the arc
If an angle’s vertex is on the circle, it’s measure is
1/2 the measure of it’s arc
If an angle’s vertex is on the interior of the circle, it’s measure is…..
1/2 (sum of arc)
If an angle’s vertex is on the exterior of the circle, it’s measure is….
1/2 (difference of arcs)
chord segments
two chords that intersect inside a circle, each chord being divided into 2 segments
secant segment
segment of a secant line that has exactly one endpoint on the circle
If 2 chords intersect in a circle, their _______ are equal
products
external secant segment
secant segment that lies on the outside of the circle with one endpoint on the circle
If 2 secants intersect on the outside of the circle, you…..
multiply the outside (external secant segments) by the outside plus the inside (x(x+y)) and those equal each other
If a tangent and a secant intersect in the exterior of a circle, the _______ equals the _______
square of tangent, product of secant and ESS
“Completing the square” Formula
(b/2)^2
Equation of a Circle in Standard Form
(x-h)^2 + (y-k)^2 = r^2
