Circle Proofs

Allie Buksha6-9-09

GeometryMr. Chester

VOCABULARY RADIUS- a line segment drawn from the center point to

a point on the circle DIAMETER – a line segment from one point on the circle

to another, and passes the center point SECANT – a line segment drawn from an external point

to a point on the circle while passing through the circle once.

TANGENT– a line segment drawn from an external point to a point on the circle, and it extended wont intersect the circle again

CHORD – a line from one point on the circle to another

TYPES OF ANGLES

INSCRIBED ANGLES – an angle formed by two chords with the vertex on the circle

CENTRAL ANGLES – an angle formed by two radii with the vertex on the circle

THEOREOMS All radii of a circle are congruent

In a circle, congruent central angles have congruent arcs

In a circle, congruent arcs have congruent chords and vice versa

A diameter perpendicular to a chord bisect the chord and its arcs

Congruent chords in the same circle are equidistant from the center of the circle

In a circle, if two chords are unequal, the shorter chord is farther from the center

An angle inscribed in a semicircle is a right angle

In a circle, inscribed angles that intercept the same arc are congruent

Parallel lines intercept congruent arcs

If a line is tangent to a circle then it is perpendicular to the radius at that point

Two tangent segments drawn to a circle from an external point are congruent

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