Circle Theorems

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What is the central angle of a circle?

The central angle is an angle whose vertex is the center of the circle and whose sides are radii.

What does the Inscribed Angle Theorem state?

The Inscribed Angle Theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.

What is the relationship between the radius and a tangent at the point of tangency?

The radius is perpendicular to the tangent at the point of tangency.

What does the Alternate Segment Theorem describe?

The Alternate Segment Theorem states that the angle between a chord and a tangent is equal to the angle in the alternate segment.

What are congruent chords?

Congruent chords in a circle are chords that are equal in length.

What does the Perpendicular Bisector Theorem state in relation to chords?

It states that the perpendicular bisector of a chord passes through the center of the circle.

What is a cyclic quadrilateral?

A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

What is the property of the opposite angles of a cyclic quadrilateral?

The opposite angles of a cyclic quadrilateral add up to 180 degrees.

What is the Arc Addition Postulate?

The Arc Addition Postulate states that the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

What is the Angle at the Center Theorem?

The Angle at the Center Theorem states that the angle subtended at the center is twice that subtended at any point on the circle.

What is the significance of equal arcs in a circle?

Equal arcs in a circle subtend equal angles at the center and equal inscribed angles at the circumference.

What is the Tangent-Secant Theorem?

The Tangent-Secant Theorem states that if a tangent and a secant are drawn from an external point, the square of the tangent is equal to the product of the entire secant segment and its external part.

What is a semicircle and how is it related to angles?

A semicircle is half a circle formed by a diameter. An angle inscribed in a semicircle is a right angle.

What does the Chord Segment Theorem state?

The Chord Segment Theorem states that when two chords intersect, the products of the lengths of their segments are equal.

What does the Tangent-Tangent Theorem state?

The Tangent-Tangent Theorem states that two tangent segments drawn from an external point to a circle are equal in length.