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Geometry Chapter 10
Geometry For Enjoyment and Challenge Chapter 10 Axioms
| Question | Answer |
|---|---|
| Theorem 74 | If a radius is perpendicular to a chord, then it bisects the chord. |
| Theorem 75 | If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord. |
| Theorem 76 | The perpendicular bisector of a chord passes through the center of the circle. |
| Theorem 77 | If two chords of a circle are equidistant from the center then they are congruent. |
| Theorem 78 | If two chords of a circle are congruent, then they are equidistant from the center of the circle. |
| Theorem 79 | If two central angles of a circle are congruent, then their intercepted arcs are congruent. |
| Theorem 80 | If two arcs of a circle are congruent, then the corresponding central angles are congruent. |
| Theorem 81 | If two central angles of a circle are congruent, then the corresponding chords are congruent. |
| Theorem 82 | If two chords of a circle are congruent, then the corresponding chords are congruent. |
| Theorem 83 | If two arcs of a circle are congruent, then the corresponding chords are congruent. |
| Theorem 84 | If two chords of a circle are congruent, then the corresponding arcs are congruent. |
| Theorem 85 | If two tangent segments are drawn to a circle from an external point, then those segments are congruent. |
| Theorem 86 | The measure of an inscribed angle or a tangent chord angle is one-half the measure of an intercepted arc. |
| Theorem 87 | The measure of a chord-chord angle is one half of the sum of the measures of the arcs intercepted by the chord-chord angle and its a vertical angle. |
| Theorem 88 | The measure of a secant-secant angle, a secant-tangent angle, or tangent-tangent angle is one-half the difference of the measures of the intercepted arcs. |
| Theorem 89 | If two inscribed or tangent-chord angles intercept the same arc, then they are congruent. |
| Theorem 90 | If two inscribed or tangent-chord angles intercept congruent arcs, then they are congruent. |
| Theorem 91 | An angle inscribed in a semicircle is a right angle. |
| Theorem 92 | The sum of the measures of a tangent-tangent angle and its minor arc is 180. |
| Theorem 93 | If a quadrilateral is inscribed in a circle, its opposite angles are supplementary. |
| Theorem 94 | If a parallelogram is inscribed in a circle, it must be a rectangle. |
| Theorem 95 | If two chords of a circle intersect inside the circle then the product of the measures of the segments of the one chord is equal to the product of the measures of the segments of the other chord |
| Theorem 96 | If a tangent segment and a secant segment are drawn from an external point of a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part. |
| Theorem 97 | If two secant segments are drawn from an external point to a circle, then the product of the measures of one secant segment and its external part is equal to the product of the measures of the other secant segment and its external part. |
| Theorem 98 | The length of an arc is equal to the circumference of its circle times the fractional part of the circle determined by the arc. |
Created by:
kroogn20
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