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C HORDS, S ECANTS, AND T ANGENTS 10.1 & 10.3

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S ECANT A secant is a line that intersects a circle in two points. A tangent is a line that intersects the circle in exactly one point. T ANGENT

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C HORDS, S ECANTS, AND T ANGENTS Secant Chord Tangent

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C OMMON T ANGENTS A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.

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T HEOREM The tangent of a circle is perpendicular to radius at the point of tangency.

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U SING T ANGENT L INES

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T HEOREM Tangent segments from a common external point are congruent.

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T HEOREM In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

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T HEOREM If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

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T HEOREM 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

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W HAT IS THE MEASURE OF A RC CD IN THE FIGURE BELOW ?

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T HEOREM In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

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W HAT IS THE VALUE OF X FOR THE CIRCLE BELOW ?

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Chapter 7 Circles. Circle – the set of all points in a plane at a given distance from a given point in the plane. Named by the center. Radius – a segment.

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