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All radii of the same circle are _________. |
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All radii of the same circle are congruent |
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| A central angle is an angle whose vertex is ____________. |
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| A central angle is an angle whose vertex is the center of the circle. |
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A minor arc is an arc that measures less that 180 degrees. |
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| A major arc is an arc whose measure is greater than 180 degrees. |
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In a circle or in congruent circles, congruent central angles intercept congruent arcs. |
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| In a circle or in congruent cirlces, congruent arcs are intercepted by congruent central angles. |
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| In a circle or in congruent circles, congruent central angles have congruent chords. |
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| In a circle or in congruent circles, congruent arcs have congruent chords. |
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| In a circle or in congruent circles, congruent chords have congruent central angles. |
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In a circle or in congruent cirlces, congruent chords have congruent arcs. |
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| A diameter perpendicular to a chord bisects the chord and its arcs. |
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| If two chords of a circle are congruent, they are equidistant from the center of the circle. |
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If two chords of a circle are equidistant from its center, they chords are congruent. |
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| Definition of an inscribed angle. |
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An inscribed angle equals half the measure of the intercepted arc m ABC = 1/2 (mAC) |
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The measure of an inscribed angle of a circle is equal to one-half the measure of its intercepted arc.
Case 1 The center of the circle is a point on one ray of the inscribed angle
Case 2 The center of the circle is a point in the interior of the inscribed angle
Case 3 The center of the circle is a point in the exterior of the inscribed angle |
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| An angle inscribed in a semicircle is a right angle. |
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| Two inscribed angles of a circle that intercept the same arc are congruent. |
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At any given point on a circle there is ___ and only ___ tangent to the circle |
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| one and only one tangent to the circle |
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| If a line is perpendicular to the radius at its point of intersection with the circle, then the line is tangent to the circle. |
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| If a line is tangent to a circle, the line is perpendicular to the radius drawn to the point of tangency. |
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| Tangent segments drawn to a circle from an external point are congruent. |
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| If two tangents are drawn to a circle from an external point, the line determined by that point and the center of the circle bisects the angle formed by the tangents. |
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The measure of an angle formed by a tangent and a chord intersecting at the point of tangency is equal to one-half the measure of the intercepted arc. m SPR = 1/2 (mPR) |
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The measure of an angle formed by two chords intersecting within a circle is equal to one-half the sum (average) of the measures of the arcs intercepted by the angle and by its vertical angle. m AED = 1/2 (mAD+mBC) |
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The measure of an angle formed by Case 1, Case 2, or Case 3 (see below) is equal to half the difference of the measures of the intercepted arcs.
Case 1 An angle formed by a tangent and a secant
Case 2 An angle formed by two secants
Case 3 An angle formed by two tangents |
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| If two chords intersect within a circle, the product of the measures of the segments of one chord equals the product of the measures of the segments of the other chord. |
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| If a tangent and a secant are drawn to a circle from an external point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external segment. |
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| If two secants intersect outside a circle, then the product of the measures of one secant segment and its external segment is equal to the product of the measures of the other secant segment and its external segment. |
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