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Part 9

 Corollary 4 The opposite angles of an inscribed quadrilateral are supplementary. Theorem 11.11 The measure of an angle formed by two secants or chords intersecting in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Theorem 11.12 The measure of an angle formed by two secants intersecting in the exterior of the circle is one-half the difference of the measures of the intercepted arcs. Theorem 11.13 If a tangent and a secant (or a chord) intersect at the point of tangency on a circle, then the measure of the angle formed is one-half the measure of its intercepted arc. Theorem 11.14 The measure of an angle formed either by (1) a tangent and secant intersecting at a point exterior to a circle, or (2) two tangents intersecting at a point exterior to a circle equals one-half the difference of the measures of the intercepted arcs. Theorem 11.15 If two chords of a circle intersect, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. Theorem 11.16 If a tangent and a secant intersect in the exterior of a circle, then the square of the length of the tangent segment equals the product of the lengths of the secant segment and the external secant segment. Corollary If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. Theorem 11.17 The equation of a circle with the coordinates of the center (b,k) and a radius of length r is (x - h)' + (y - k)l = r. Postulate 20 Congruent polygons have equal areas. Postulate 21 The area of a rectangle is the product of the lengths of a base and a corresponding altitude (Area of rectangle = bb). Theorem 12.1 The area of a square is the square of the length s of a side (A = S2). Postulate 22 Area Addition Postulate: If a region is the union of two or more nonoverlapping regions, then its area is the sum of the areas of these nonoverlapping regions. Theorem 12.2 The area of a parallelogram is the product of the lengths of a base and a corresponding altitude (Area of parallelogram = bb). Theorem 12.3 The area of a triangle is one-half the product of the lengths of a base and a corresponding altitude (Area of triangle = lbh).

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Note: The concepts in this collection may not be entirely accurate.
They are for reference only.