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Geometry chapter 10!
chapter ten theorem's and equations and formulas
| Question | Answer |
|---|---|
| Theorem 10.1 | in a plane, a line is a tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle |
| Theorem 10.2 | Tangent segments from a common external point are congruent |
| Key Concepts | Measuring Concepts: the measure of a minor arc is the measure of its central angle. the expression mAB is read as "the measure of arc AB". mADB=360 ○-the measure of the related minor arc |
| Theorem 10.3 | in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. AB=CD if&only if AB-CD |
| Theorem 10.4 | if one chord is a perpendicular bisector of another chord then the first chord is a diameter |
| Theorem 10.5 | if a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc |
| Theorem 10.6 | in the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center |
| Theorem 10.7 | the measure of an inscribed angle is one half the measure of its intercepted arc. |
| Theorem 10.8 | if two inscribed angles of a circle intercept the same arc, then the angles are congruent. |
| Theorem 10.9 | if a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. |
| Theorem 10.10 | a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. |
| Theorem 10.11 | if a tangent and a chord intersect at a certain point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. m<1=1/2mAB m<2=1/2mBCA |
| Theorem 10.12 | if two chords intersect inside a circle, then the measure of each anlge is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle m<1=1/2(mDC+mAB) m<2=1/2(mAD+mBC) |
| Theorem 10.13 | if a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of teh angle formed is one half the difference of the measures of the intercepted arcs. m<1=1/2(mBC-mAC) m<2=1/2(mPQR-mPR) m<3=1/2(mXY-mWZ) |
| Theorem 10.14 | if two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chords. EA*EB=EC*ED |
| Theorem 10.15 | if two secants share the same endpoint outside a circle, then the product of the lengths of one secant s segment and its external segment equals the product of the lengths of the other secant segments and its external segment |
| Theorem 10.16 | if a secant and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment EA2=EC*ED |
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Aly(:
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