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chapter 10 rules (Theorems (10.2 In the same circle or in congruent circle…
chapter 10 rules
Theorems
10.2 In the same circle or in congruent circle two minor arcs are congruent if and only if their corresponding chords are congruent
10.3 if a diameter (or radius) of a circle is perpendicular to a chord then it bisect the chord and its arc
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10.5 in the same circle or in congruent circles two chords are congruent if and only if they are equidistant from the center
10.6 if an angle is inscribed in a circle then the measure of the angle equals one half the measure of intercepted arc
10.7 if two inscribed angles of a circle intercept the same arc or congruent arcs then the angles are congruent
10.8 An inscribed angle of a triangle intercepts a diameter or semicircle if and only if it angle is a right angle
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Theorems
10.0 in a plane a line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency
10.12 it two secants or chord 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
10.13 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 intercepted arc
10.14 if two secants 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 measure of the intercepted arcs
10.15 if two chords intersect in a circle then the product of the length of the chord segments are equal
10.16 if two secants intersect in the exterior of a circle then the product of the measure of one segment and its external secant segment is equal to the product of the measure ion the other secant and its external secant segment
10.17 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 measure of a scant and its external secant segment
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circumference
if a circle has diameter d or radius r the circumference C equal the diameter times pi or twice the radius times pi
sum of central angle
the sum of the measure of the measure of the central angles of a circle with no interior points in common
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Arc length
The ratio of the length of an arc (l) to the circumference of the circle is equal to the ratio of the degree measure of the arc to 360
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