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Rules of chapter 10 (10.1 Special segments in a circle (Circle pairs (Two…
Rules of chapter 10
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10.3
In the same circle or incongruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
If a diameter (or radius) of a circle is perpendicular to a chord ,then it bisects the chord and its arc
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In the same circle or n congruent circles, two chords are congruent if and only if they are equidistant from
10.6
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If two secant 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 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 intersected arc.
If two secant , a secant and a tangent ,or two tangents intersects 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.
10.5
Tangent: is a line in the same plane as a circle that intersects the circle in exactly one point.called the point of tangency
A common tangent: Is a line ,ray, or segment that is tangent to two circles in the same plane.
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
10.7
If two 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 products of the measures of one secant segment and it 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 intersects 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 .
10.4
Inscribed angle theorem
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 supplementry
If tw inscribed angles of a circle intercept the same arc or congruent arcs, the angles are congruent
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc
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