Circles (other)
Overview
Important
Circles have many associated elements beyond the center and radius. Important ones include: chords, secants, tangents, arcs, sectors (region between two radii and the arc), and segments (region between a chord and the arc). Tangents are perpendicular to the radius at the point of contact. The power of a point theorem relates lengths of segments created by chords, secants, and tangents.
Important properties
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A tangent to a circle is perpendicular to the radius at the point of contact.
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Equal chords are equidistant from the center.
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The angle in a semicircle is a right angle.
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The power of a point theorem: For a point outside a circle, the product of the lengths of the segments of a secant equals the square of the length of the tangent from that point.