Section 10.1 Theorem 74- If a radius is perpendicular to a chord, then it bisects the chord Theorem 74- If a radius is perpendicular to a chord, then it.

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Presentation transcript:

Section 10.1 Theorem 74- If a radius is perpendicular to a chord, then it bisects the chord 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 a chord Theorem 76- The perpendicular bisector of a chord passes through the center of a circle

Section 10.2 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

Section 10.3 Theorem 79- If two central angles of a circle (or of congruent circles) are congruent, then their intercepted arcs are congruent. Theorem 80- If two arcs of a circle (or of congruent circles) are congruent, then the corresponding central angles are congruent. Theorem 81- If two central angles of a circle (or of congruent circles) are congruent, then the corresponding chords are congruent.

Theorem 82- If two chords of a circle (or of congruent circles) are congruent, then the corresponding central angles are congruent Theorem 83- If two arcs of a circle (or of congruent circles are congruent, then the corresponding chords are congruent. Theorem 84- If two chords of a circle (or of congruent circles) are congruent, then the corresponding arcs are congruent.

Section 10.4 Theorem 85- If two tangent segments are drawn to a circle from an external point, then those segments are congruent.

Section 10.5 Theorem 86- The measure of an inscribed angle or a tangent- chord angle (vertex on a circle) is one half the measure of its intercepted arc. Theorem 87- The measure of a chord-chord angle is one-half the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle. Theorem 88- The measure of a secant-secant angle, a secant-tangent angle, or a tangent-tangent angle (vertex outside the circle) is one half the difference of the measures of the intercepted arcs.

Section 10.6 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 semi-circle is a right angle.

Theorem 92- The sum of the measures of a tangent-tangent angle and its minor arc is 180.

Section 10.7 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.

Section 10.8 Theorem 95- If two chords of a circle intersect inside the circle, then the product of the measures of the segments of 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 eternal point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and the 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 scant segment and its external part is equal to the product of the measures of the other secant segment and its external part.

Section 10.9 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. Length of PQ= ( )πd mPQ 360