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# Geometry chapter 10!

### chapter ten theorem's and equations and formulas

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
Created by: Aly(: