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Circle Chapter Notes Mr. Durkin ANGLES AND SEGMENTS INVOLED IN CIRCLES Radius – Segment from the center of a circle to the outer edge Diameter - Segment from one side of a circle to another passing through the center. Chord – Segment that touches both sides of the circle. Secant – Segment that starts on the outside of a circle and passes through the circle touching both sides. Tangent – Line that is outside the circle and touches it at one point. Central Angle – Angle formed at the center of a circle by a radius or diameter Inscribed Angle – Angle formed on the inside of the circle with it’s vertex on the circles edge. ANGLES AND ARCS OF A CIRCLE Central Angles – Equal to the arc that it intercepts Inscribed angles – Equal to ½ the arc that it intercepts Inscribed angle that touches both sides of a diameter must form a right angle. Angle formed by a tangent and a radii or diameter form a right angle on the edge of a circle. Two inscribed angles that intercept the same arc are congruent. Angles formed outside the circle equal ½ the difference of the two arcs that it intercepts The angle can be formed by either 2 tangents, 2 secants, or a tangent and a secant. Angles formed inside the circle equal ½ the sum of the two arcs that it Intercepts. The angle is formed by 2 chords. THE MEASURE OF SEGEMENTS THAT ARE IN A CIRCLE If two chords intersect in a circle, the product of the segments of one chord must equal the product of the segments of the other. If one of the chords is a diameter and it is perpendicular to another chord, it bisects the chord. If 2 secants intersect outside of the circle, the product of the measure of the one secant and the segment outside the circle is equal to the other secant and it’s segment outside the circle. If 2 tangents intersect outside the circle, they must be equal. If a tangent and a secant intersect outside the circle, the tangent squared equals the product of the secant and it’s outside segment.