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What does the angle subtended by an arc at the center of a circle equal compared to the angle subtended by the same arc at the circumference?
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It is twice the angle subtended at the circumference.
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State the Alternate Segment Theorem.
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The angle between the tangent and the chord at the point of contact is equal to the angle in the alternate segment.
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What is the Angle in a Semicircle Theorem?
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A triangle inscribed in a semicircle is a right triangle, with the right angle opposite the diameter.
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State the Congruent Chords Property.
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Equal chords in a circle subtend equal angles at the center.
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What can be said about angles in the same segment?
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Angles in the same segment of a circle are equal.
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If two tangents are drawn to a circle from an external point, what can be said about their lengths?
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The two tangents drawn from an external point are equal in length.
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What is the Angle Between Radius and Tangent Theorem?
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The angle between the radius and tangent at the point of contact is 90 degrees.
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Explain the concept of a Cyclic Quadrilateral.
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A quadrilateral is cyclic if its vertices all lie on the circumference of a circle.
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What is special about the opposite angles of a cyclic quadrilateral?
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The opposite angles of a cyclic quadrilateral add up to 180 degrees.
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State the Perpendicular from the Center Theorem.
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A line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.
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Describe the relationship between an arc and its chord.
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The angle subtended at the center by an arc is larger than the angle subtended by the same arc at any other point on the circle.
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What does the Power of a Point Theorem state?
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For a point outside a circle, the product of the lengths of the two line segments from the point to the points of intersection of a line with the circle is constant.
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What is a tangent?
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A line that touches a circle at exactly one point.
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How do you prove two lines are tangents if they meet a circle at a point?
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Show that both angles formed with the radii are 90 degrees.
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State the Equal Arcs Property.
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If two arcs of a circle are equal, then the chords of those arcs are also equal.
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