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# Circles

### postulates and theorems relating to circles (chp. 10)

HypothesisConclusion
Two arcs are congruent if and only if their corresponding central angles are congruent
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
In a circle, if the diameter (or radius) is perpendicular to a chord then it besects the chord and its arc
In a circle or in congruent cirlces, two chords are congruent if and only if they are quidistant from the center
If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc ( or the measure of the intercepted arc is twice the measure of the inscribed angle)
If two inscribed angles of a circle (or congruent circles) intercept congruent arcs (or the same arc), then the angles are congruent
If an inscribed angle intercepts a semicircle, the angle is a right angle
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency
If a line is perpendicular to a radius of a circle at its endpoint on the circle then the line is tangent to the circle
If two segments from the same exterior point are tangent to a circle then they are congruent
If two secants 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
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
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 positive difference of the measures of the intercepted arcs
If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal
If two secent segments are drawn to a circle from an exterior point, 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 segment and its external secant segment
If a tangent segment and a secant are drawn to a circle from an exterior point, then the square of the measure of a tangent segment is equal to the product of the measures of the secant segment and its external secant segment
Created by: m.meyer