Circles and Tangents in GeometryA series of free High School Geometry Video Lessons from Brightstorm.
Radii to Tangents When a radius is drawn to a point of tangency, the angle formed is always a right (90 degree) angle. This fact is commonly applied in problems with two tangent segments drawn to a circle from a point. If two radii to tangents are drawn in, a kite with two right angles is formed and the missing angles or sides can be found. Related topics include central angles, tangent segments to a circle, and chords.
Tangent Segments to a Circle A tangent intersects a circle in exactly one point. When two segments are drawn tangent to a circle from the same point outside the circle, the segments are congruent. The extension problem of this topic is a belt and gear problem which asks for the length of belt required to fit around two gears. Topics related to circle radii include inscribed circles and radii to tangents.
Inscribed Angles Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc. Inscribed angles that intercept the same arc are congruent.
Angles in Semicircles and Chords to Tangents If an angle is inscribed in a semicircle, it will be half the measure of a semicircle (180 degrees), therefore measuring 90 degrees. Angles in semicircle is one way of finding missing missing angles and lengths. Pythagorean's theorem can be used to find missing lengths (remember that the diameter is the hypotenuse). Also, the measure of an angle formed by a chord to a tangent is half the intercepted arc.
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