Geometry Circles
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What is a circle?
The set of points that are equidistant from a given point. It is not a polygon because it does no have sides.

What is a radius?
The distance from the center of the circle a point on the circle. All radii are congruent in a circle.

What is a chord?
A segment whose endpoints are on a circle.

What is a diameter?
A chord that passes through the center of the circle. It is the longest chord in a circle.

What is a secant line?
A line that intersects a segment in two points. It goes on through the circle.

What is a tangent?
A line that intersects the circle in exactly one point.

What are tangent circles?
Circles that intersect at one point.

What are concentric circles?
Circles with no point of intersection and share the same intersection.

What is a common tangent?
A tangent that touches two circles. There can be between 0 and 4 common tangents between circles. Try to draw a picture for a situation of each.

What do ouknow about radii and tangents?
The tangent line is perpindicular to the radius that touches the point of tangency.

What do you know about tangents to a circle that intersect (Party Hat Theorem).
The tangents are congruent to each other.

What do you know about central angles?
They are angles with their vertices on the center of the circle. They form arcs that have the same measure as the central angle.

What is a minor arc?
An arc that is less than 180^{o}. A minor arc has only two points in notation.

What is a major arc?
An arc with more than 180^{o}. It is notated with three points and you must figure it out by going around the circle.

What is a semicircle?
An arc whose endpoints are on a diameter and it is 180^{o}.

What makes congruent circles?
Equal radii

What makes congruent arcs?
Arcs of the same measure that are on the same circle or are on two congruent circles.

What do you know about about the measures of two minor arcs if the chords that make them are congruent?
The arcs are congruent.

What do you know about a diameter that is perpendicular to a chord?
The diameter bisects the chord and the arc that the chord makes.

What do you know about chords that are equidistant from the center of a circle?
The chords are congruent.

What is an inscribed angle?
An angle with its vertex on the circle and the sides contain chords of the circle.

What is an intercepted arc?
The arc on the interior of an inscribed angle.

What is an inscribed angle?
It is half of the arc that it makes.

What do you know about inscribed angles that share the same arc?
They are congruent.

What do you know about an inscribed quadrilateral?
Its opposite angles are equal to 180^{o}, or are supplementary.

What do you know about chords and tangents that inersect?
The angles that the lines make are half of themeasure of the intersepted arc.

What dou you know aboutthe measure of the angles inside a circle id it is not in the center or on the circle?
The measure of each angle is the average of the arcs that are intercepted by the angle and its vertical angle.

What do you know about the measure of angles outside of a circle that are formed by tangents or secants?
The measure of the angle formed is one half the DIFFERENCE of the measures of the intercepted arcs.

What are the lengths of two intersecting chords equal to?

What is the length of an intersecting tangent and secant?

What is the length of two intersecting secants?

What is the equation of a circle?
where r is the radius, h is the x coodinate of the center of the circle, and k is the y coordinate of the center of the cirlce.