Circles in GeometryA series of free High School Geometry Video Lessons from Brightstorm.
Cyclic Quadrilaterals and Parallel Lines in Circles A cyclic quadrilateral has vertices on the same circle and is inscribed in the circle. The opposite angles have the same endpoints (the other vertices) and together their intercepted arcs include the entire circle. Since the measure of an inscribed angle is half the intercepted arc, the sum of the opposite angles must be 180 degrees.
Circumference Circumference can be thought of as the "perimeter" of a circle or the distance around a circle. Since pi is the ratio of circumference to diameter, circumference can be calculated by multiplying the circle's diameter by pi. Another formula substitutes d = 2r, where one diameter equals two radii, and C = 2(r)(pi). Related topics include area of a circle, arc length, and parts of a circle.
Arc Length Commonly confused with arc measure, arc length is the distance between the endpoints along the circle. Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle and calculated that way: find the circumference of the circle and multiply by the measure of the arc divided by 360.
Secants A secant is a line, ray, or line segment that intersects a circle in two places. Three points are covered: (1) secants that intersect in a circle which divide each other proportionally, (2) the angle formed by secants which intersects in a circle and is half the sum of the intercepted arcs, and (3) two secants drawn from the same point outside a circle that form an angle whose measure is half the difference of the intercepted arcs.
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