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(10.6 (VOCAB, If two secants or chords intersect in the
interior of a…
10.6
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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.
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.
10.4
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
An inscribed angle of a triangle intercepts a diameter or semicircle if and only if the angle is a right angle.
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
10.7
If two chords intersect in a circle, then the products
of the lengths of the chord segments are equal.
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.
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.
10.2
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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.
l = x/360 x 2pir
10.5
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.
If two segments from the same exterior point are tangent to a circle, then they
are congruent.
10.3
In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
In the same circle or in congruent circles, two chords
are congruent if and only if they are equidistant from F the center.
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