Circles Flashcards
What is a tangent
In the plane of a circle that intersects the circle in exactly 1 place
What is a chord
A segment who’s endpoints are on the circle
What is a secant
A line that intersects a circle in 2 spots
What do 2 circles have to look like to share 3 common tangents
They have to be touching but not overlapping
What do 2 circles have to look like to have 2 common tangents
Not touching (but not inside of one another) or overlapping
What do 2 circles have to look like to have 1 common tangent
They have to be inside of one another and touching at 1 point
What do 2 circles have to look at to have no tangents in common
1 has to be inside of the other
A line is only a tangent if it is ____________ to a radius at its endpoint on the circle
Perpendicular
Two tangents coming from the same external point are?
Congruent
What is a major arc and how is it classified?
An arc measuring more than 180 degrees and with 3 letters on the arc
What is a minor arc and how is it classified
An arc that is less than 180 degrees and with 2 letters
2 minor arcs are congruent only If?
Their chords are congruent
If one chord is perpendicular to another then the second chord is?
A diameter
If a diameter is perpendicular to a chord then…?
It bisects the chord and it’s arc
2 chords are congruent if and only if…?
They are equidistant from the center
What is an inscribed angle
An angle with a vertex on the circle and sides made of chords
What is an intercepted arc
The arc made by an inscribed angle that has endpoints on the angle
What is an inscribed polygon
A polygon that lies in a circle and had all vertices on the circle
What is a circumscribed circle?
The circle that contains an inscribed polygon and it’s vertices
How does the measure of an inscribed angle compare to the measure of its arc?
The arc is twice the measure of the angle
If 2 inscribed angles intercept the same arc then…..?
The angles are congruent
A quadrilateral can be inscribed in a circle if and only if…?
It’s opposite angles are supplementary
If a tangent and chord intersect on a circle then the measure if each angle is…?
Half of the measure if it’s intercepted arc
How do you find the measure of an angle of 2 chords that intersect
Average the measure of the arcs made by the angle and it’s vertical angle
How do you find the lengths of 2 intersecting chords?
Multiply the segments of the chords together and set them equal,to each other
How do you find the lengths of 2 secants, tangents or a secant and a tangent coming from the same point?
Multiply the tangent times the whole line and set them equal to each other
What is the standard equation of a circle?
(X-h)2+(y-k)2=r2
What does (h,k) stand for in the standard equation of a circle?
The coordinates of the center of the circle
What does the point (x,y) stand for in the standard equation of a circle?
Any point on the circle
What does r2 stand for in the standard equation of a circle
The radius of the circle squared
