Honors Geometry Unit 8

What is the circumference formula using radius

C=2pie*r

What is the circumference formula using diameter

C=pie*d

What is the equation for the length of an arc?

Angle/360×2Pie*r

What is the formula for the area of the sector

Angle/360 x pie* r (squared)

Chord

Any segment with both endpoints on the circles

Diameter

A chord that passes through the center of the circle

Minor arc

An arc that measures less than 180

Major arc

An arc that measures greater than 180

Semicircle

An arc that measures exactly 180

Central angle

Has the center of the circle as its vertex and 2 radii as sides

Arc Addition postulate

Two adjacent arcs can add to form a larger arc

Arc length

Distance between 2 point on a circle

-A fraction of the circumference

Theorem 1

2 minor arc are congruent if and only if their corresponding chords are congruent

Theorem 2

If a diameter or radius is perpendicular to a chord then it bisects the chord and its arc

Theorem 3

2 chords are congruent only if they are equidistant from the center

Arc length formula

Angle/360 x2pieR

Area of sector formula

Angle/360. XpieR squared

Inscribed angle

An angle that has its vertex on the circle and its sides a chords

If an angle is inscribed then

The measure is ½ the measure of the intercepted arc

Inscribed angle formula

X=1/2n

If two inscribed angles intercept congruent arcs or the same arc then

The angles are congruent

If a quadrilateral is inscribed angles intercept congruent then

It’s opposite angles are supplementary (add to 180)

Tangent

A line intersecting the circle in exactly 1 point. This is the point of tangency

Perpendicular tangent theorem

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

• If the Pythagorean theorem works then it is a right triangle and so the line is tangent

Ice cream cone theory

If two segments from the same exterior point are tangent to a circle, then they are congruent

Secant

A line that intersects the circle in exactly 2 points