Circles

C-74 - Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to the point of tangency. (pg. 453)

C-75 - Tangent Segment Conjecture

Tangent segments to a circle from a point outside the circle are congruent. (pg. 454)

C-76 - Chord Central Angles Conjecture

If two chords in a circle are congruent, then they determine two central angles that are congruent. (pg. 459)

C-77 - Chord Arcs Conjecture

If two chords in a circle are congruent, then their intercepted arcs are congruent. (pg. 459)

C-78 - Perpendicular to a Chord Conjecture

The perpendicular from the center of a circle to a chord is the bisector of the chord. (pg. 460)

C-79 - Chord Distance to Center Conjecture

Two congruent chords in a circle are equidistant from the center of the circle. (pg. 460)

C-80 - Perpendicular Bisector of a Chord Conjecture

The perpendicular bisector of a chord passes through the center of the circle. (pg. 460)

C-81 - Inscribed Angle Conjecture

The measure of an angle inscribed in a circle is one-half the measure of the intercepted arc. (pg. 465)

C-82 - Inscribed Angles Intercepting Arcs Conjecture

Inscribed angles that intercept the same arc are congruent. (pg. 466)

C-83 - Angles Inscribed in a Semicircle Conjecture

Angles inscribed in a semicircle are right angles. (pg. 466)

C-84 - Cyclic Quadrilateral Conjecture

The opposite angles of a cyclic quadrilateral are supplementary. (pg.467)

C-85 - Parallel Lines Intercepted Arcs

Coniecture

Parallel lines intercept congruent arcs on a circle. (pg. 467)

C-86 - Circumference Conjecture

If C is teh circumference and d is the diameter of a circle, then there is a number a such that C = nd. If d = 2r where r is the radius, the C = 2mr. (pg.477)

C-87 - Arc Length Conjecture

The length of an arc equals the measure of the arc divided by 360° times the circumference. (pg. 482)

tangent segments

A line segment that lies on a tangent line with one endpoint at the point of tangency. (pg. 453)

intercepted arc

An arc that lies in the interior of an angle with endpoints on the sides of the angle. (pg. 454)

tangent circles

Circles that are tangent to the same line at the same point.. They can be internally tangent or externally tangent. (pg. 455)

cyclic quadrilateral

A quadrilateral that can be inscribed in a circle. (pg. 467)

secant

A line that intersects a circle in two points. (pg. 467)

circumference

The perimeter of a circle, which is the distance around the circle. Also, the curved path of the circle itself. (pg.476)

arc length

The portion of the circumference of the circle described by an arc, measured in units of length. (pg. 481)

radian measure

The ratio found by dividing the length of the arc by its radius. (pg. 482)

circumscribed

shape inside a circle

inscribed

circle inside a shape

arc length formula

l = m/360 2(pi)r