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