Circle study set

Semi-circle

half of a circle.

Straight angle

A line that equals 180 degrees.

Tangent

A line that intersects a circle at exactly one point.

Circumscribed polygons

A polygon is circumscribed about a circle of every side of the polygon is tangent to the circle.

Inscribed angles

An angle whose vertex is on the circle and whose sides are chords of the circle. This angle is half of the measure of the intercepted arc.

Arc addition postulate

An arc formed by two adjacent arcs equal to the measure of the arcs added together.

Intercepted angles

An arc on the interior of an inscribed angle and could be a major or a minor. ( x would be the example in image)

Angle formed outside of a circle by intersection

Angle formed outside of a circle by intersection = 1/2 the distance of intersection. * two tangents *two secants * a tangent and a secant.

Angles formed by two angles

Angles formed by two angles = 1/2 the sum of intercepted arcs.

Central angle

Angles whose vertex is the center of the circle.

Congruent arcs

Arcs are congruent if their central angles are congruent and the circles are the same size.

Arcs

Central angles create an arc on the center of a circle.

Concentric Circles

Circles that share a center

Theorem #1

If 2 chords intersect in the interior of a circle, then the product of the length of the segment of one chord is equal to the product of the lengths of the segments of the other chord.

Converse

If a line is perpendicular to a radius of a circle than it is a tangent.

Theorem #3 ( Secant Segment)

If a secant segment and a tangent segment 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.

Ice cream cone theorem

If two segments from the same external points are tangent to a circle, then the segments are congruent.

Theorem#2 ( Tangent Secant)

If two segments share the same endpoint outside the circle then the product of the length of 1 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.

Tangent chord angle

Tangent chord angles= 1/2 intercepted arc.

Internally Tangent

Tangents that cross between the circles center ( blue in the image).

Externally Tangent

Tangents that don't cross between the circles center. ( pink in the image)

Major arc

The exterior of the central angles between 180 degrees and 360 degrees.

Point of tangency

The point where the line is tangent to the circle.

Slices

Two types: sector(pizza) and segment ( made by a chord).

Angle formed by two intercepting chords

When two chords intersect a circle, four angles are formed. At the point, if intersection, two sets of congruent vertical angles are formed in the corner or the x that appears.

segments of a chord

When two chords intersect in the interior of a circle each chord is divided into two segments.

Inscribed quadrilateral

a quadrilateral can be inscribed in a circle in and only if the opposite angles are supplementary.

Minor arc

less than 180 degrees.