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Unit 10 math test- concepts

What are all radii of a circle equal to?

each other

Radius formula

r= d/r or r= 1/2*d

Diameter formula

d= 2r

Relationship of congruent circles and their radii

their radii are congruent

Are all circles similar

yes

circumference formula

C= d (pie) or C= 2r(pie)

Sum of all the central angles in a circle

360 degrees

Relationship between arc angles and their central angles

they are congruent

formula for a major arc

360- the major arc measure

What is the measure of a semicircle

180 degrees

The measure of an arc formed by two adjacent arcs is

the sum of the measures of the two arcs

finding the angle of a circle graph percentage

percent/100 = arc degrees/360

formulas for finding the ar length

L / 2(pie)r = x/360 or L= x / 360 * 2(pie)r

When are 2 minor arcs congruent in the same circle

if their chords are congruent

What happens if a diameter (or radius) of a circle is perpendicular to a chord

it bisects the chord and it's arc

When are two chords in congruent circles or the same circles congruent?

if and only if they are equidistant from the center

What happens to an angle's measure if it is inscribed in a circle?

the measure of the angle equals one-half the measure of its intercepted arc

What happens if two inscribed angles of a circle intercept the same arc or congruent arcs?

the angles are congruent

the formula for inscribed angle

the inscribed angle is one half of the intercepted arc

When does an inscribed angle of a triangle intercept a diameter or semicircle?

if and only if the angle is a right angle

What does it mean if a quadrilateral is inscribed in a circle?

it's opposite angles are supplementary

When is a line tangent to a circle

if and only if it's perpendicular to a radius drawn to the point of tangency

When are two segments from the same exterior point congruent

when they are tangent to the circle

What happens when two secants or chords intersect in the interior of a circle?

the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle

formula for the angles intersecting inside the circle

one half the measure of the sum of the intercepted arc

What happens if a secant and tangent intersect at the point of tangency?

the measure of each angle formed is one-half the measure of its intercepted arc

formula for the angles intersecting on the circle

one half the measure of it's intercepted arc

What happens when two secants, a secant, and a tangent, or two tangents intersect in the exterior of a circle?

the measure of the angle formed is one-half the difference between the measures of the intercepted arcs

formula for the angles intersecting outside the circle

one half the measure of the difference of the intercepted arcs

What happens when two chords intersect in a circle?

the products of the lengths of the chord segments are equal

Formula for segments of chord theorum

smaller part of chord * larger part of the same chord = the smaller part of that chord * the larger part of that chord

What happens when two secants intersect in the exterior of a circle?

the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant and its external secant segment

What happens when a tangent and a secant intersect in the exterior of a circle?

the square of the measure of the tangent is equal to the product of the secant and it's external secant segment

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