CIRCLES CIRCLES Circle a set of points equidistant

CIRCLES

CIRCLES Circle – a set of points equidistant from a central fixed point Center – the fixed point in the middle of the circle Radius - A line segment measured from the center to the edge of a circle

CIRCLES Chord – A line segment inside of the circle that has endpoints on the circle Diameter – A chord that goes through the center of the circle. It is the longest line in the circle Concentric Circles – Two or more circles that share the same center

CIRCLES Circumference – The measurement around a circle Inscribed – Shape inside of another shape Circumscribed – Circle outside of the polygon

CIRCLES

CIRCLES Central Angle – The angle between two radii in a circle Arc – Segment of the circle. Arcs are measured in degrees. It is the same measurement as the central angle. Minor Arc – Arc measure that is less than 180 Major Arc – Arc measure this between 180 & 360 Semicircle – Arc measure that is exactly 180

CIRCLES

CIRCLES Inscribed angle – An angle formed by two chords that share the same vertex on the circle. Intercepted arc – The arc created by the inscribed angle. The inscribed angle is ½ the measurement of the intercepted arc.

CIRCLES The arc is twice the measurement of the inscribed angle.

CIRCLES If two inscribed angles intercept the same arc, then the two inscribed angles are congruent.

CIRCLES If an inscribed angle of a triangle intercepts the diameter, then the angle is a right angle.

CIRCLES If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

CIRCLES Chord Theorems If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc.

CIRCLES Two chords are congruent if they are equidistant from the center.

CIRCLES Two minor arcs are congruent if their corresponding chords are congruent.

CIRCLES Tangent – a line on the same plane as the circle, that touches the circle at one point (point of tangency)

CIRCLES Common Tangent – a line on the same plane that is tangent to two or more circles

CIRCLES A line tangent to a circle is always perpendicular to the radius at the point of tangency.

CIRCLES If two lines tangent to the same circle meet at a point outside the circle, then those two lines are congruent to each other.

CIRCLES Secant – Line that cuts through the circle at two points.

CIRCLES If two chords intersect in a circle, then the products of the lengths of the chord segments are equal.

CIRCLES If two secants intersect in the exterior of a circle, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant and its external secant segment.

CIRCLES If a tangent and a secant intersect in the exterior of a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment.

CIRCLES If two secants or chords intersect in the interior of a circle, then the measure of an angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle

CIRCLES If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one half the measure of its intercepted arc. Like an inscribed angle

CIRCLES If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.