Term
|
Definition
| the set of point in a plane at a given distance from a given point in that plane. The given point is the center and the given distance is the radius |
|
|
Term
Radius
*all radii of a circle are congruent |
|
Definition
| Any segment that joins the center to a point of the circle |
|
|
Term
|
Definition
| a segment with both endpoints on a circle |
|
|
Term
|
Definition
a line that contains a chord, or
a line that intersects a circle at two points |
|
|
Term
|
Definition
| a chord that contains the center of a circle |
|
|
Term
|
Definition
| a line in the plane of a circle that intersects the circle in exactly one point, called the point of tangency |
|
|
Term
|
Definition
| the set of all points in space that are at a given distance from a given point |
|
|
Term
| Congruent Circles (or spheres) |
|
Definition
| are circles (or spheres) that have congruent radii |
|
|
Term
|
Definition
| spheres that have the same center |
|
|
Term
Theorem
If a line is tangent to a circle, then... |
|
Definition
Theorem
...then the line is perpendicular to the radius drawn to the point of tangency |
|
|
Term
Corollary
Tangents to a circle from a point are... |
|
Definition
Corollary
...are congruent |
|
|
Term
Theorem
If a line in the plane of a circle is perpendicular to a radius drawn to its endpoint on the circle, then... |
|
Definition
Theorem
...then the line is tangent to the circle |
|
|
Term
|
Definition
| an angle with its vertex at the center of the circle |
|
|
Term
|
Definition
|
|
Term
Semicircle
*semicircle or larger has to be named with 3 letters |
|
Definition
| an arc that is half of a circle |
|
|
Term
|
Definition
| smaller than a semicircle |
|
|
Term
|
Definition
| greater than a semicircle |
|
|
Term
|
Definition
arcs of the same circle that have exactly one point in common
*don't overlap, but share a point because they are right next to each other |
|
|
Term
|
Definition
Is the same as the measure of the central angle forming that arc.
*measured in degrees. |
|
|
Term
|
Definition
| the measure of the arc formed by two adjacent arcs is the sum of the measures fo these two arcs |
|
|
Term
Theorem
In the same circle or in congruent circles, two minor arcs are congruent iff (if and only if)... |
|
Definition
Theorem
...iff their central angles are congruent
**if central angles are congruent then the arcs are congruent. if arcs are congruent then the central angles are congruent |
|
|
Term
Theorem
Within a circle or in congruent circles:
|
|
Definition
|
***if you have congruent central angles, then you have congruent chords. and if you have congruent chords, then you have congruent arcs***
|
|
|
Term
Theorem
In a circle, a diameter that is perpendicular to a chord... |
|
Definition
Theorem
...bisects the chord and its arc |
|
|
Term
Theorem
Within a circle or in congruent circles: |
|
Definition
Theorem
- chords equidistant from the center are congruent
- Congruent chords are equidistant from the center
|
|
|
Term
|
Definition
| an angle with its vertex on a circle and its sides are chords of the circle |
|
|
Term
|
Definition
| The measure of an inscribed angle is equal to half the measure of it's intercepted arc |
|
|
Term
Corollary
two inscribed angles that intercept the same arc are... |
|
Definition
Corollary
...are congruent |
|
|
Term
Corollary
An angle inscribed in a semicircle is... |
|
Definition
Corollary
...is a right angle
(b/c the measure of a semicircle is 180. 180/2=90) |
|
|
Term
Corollary
If a quadrilater is inscribed in a circle, then... |
|
Definition
Corollary
...then its opposite angles are supplementary |
|
|
Term
Theorem
The measure of an angle formed by a chord and a tangent is equal to... |
|
Definition
Theorem
...is equal to half the measure of the intercepted arc |
|
|
Term
Theorem
The measure of an angle formed by 2 chords that intersect inside a circle is... |
|
Definition
Theorem
...is half the sum of the measures of the intercepted arcs
m<1= 1/2(x+y) |
|
|
Term
Theorem
The measure of an angle formed by 2 secants, two tangents, or a secant and a tangent drawn from... |
|
Definition
THeorem
...drawn from a point outside the circle is half the difference of the measures of the intercepted arcs |
|
|
Term
Theorem
For a given point and circle,... |
|
Definition
Theorem
...the product of the lengths of the 2 segments from the point to the circle is constant along any line through the point and circle |
|
|
Term
Theorem
When two secant segments are drawn to a circle from an external point,... |
|
Definition
Theorem
...the product of one secant segment and its external segment equals the product of the other secant segment and its external segment
(a+b)b=(c+d)d |
|
|
Term
Theorem
When a secant segment and a tangent segment are drawn to a circle from an external point,... |
|
Definition
Theorem
...the product of the secant segment ad its external segment is equal to the square of the tangent segment
(a+b)b=t2 |
|
|
