Circles Flashcards
If a line is tangent to a circle then -
The line is perpendicular to the radius at the point of tangency
If a line in the plane of a circle is perpendicular to a radius at it’s endpoint on the circle then-
The line is tangent to the circle
If two tangent segments to a circle share a common endpoint outside the circle then -
The two segments are congruent
Define A tangent to a circle
A line in the plane of the circle that intersects the circle in exactly one point
What do you call the point where a circle and tangent intersect
The point of tangency
Define chord
A segment whose endpoints are on a circle
Define a Central angle
An angle with its vertex at the center of the circle.
- the measure of this angle is equal to the measure of the arc that it intercepts
TRUE OR FALSE
In a circle / congruent circles central angles have congruent arcs
This also means that in a circle/ congruent circles congruent arcs have congruent central angles
True
True or false
In a circle / congruent circles central angles have have congruent chords
This also would mean that In a circle / congruent circles congruent chords have central angles
TRUE
True or false
Within a circle / congruent circles congruent chords have congruent arcs
This would also mean that within a circle / congruent circles congruent arcs have congruent chords
TRUE
True or False
In a circle/ congruent circles cords equidistant from the center/ centers are congruent
This also would mean that
TRUE
In a circle, if a diameter is perpendicular to a chord -
Then it bisects the chord and it’s arc
In a circle, if a diameter bisects a chord (that is not a diameter) -
Then it is perpendicular to the chord
In a circle, the perpendicular bisector of a chord contains -
the center of a circle
Define inscribed angle
An angle whose vertex is on the circle and whose sides are chords of the circle
Define intercepted arc
An arc with endpoints on the sides of an inscribed angle and it’s other points in the interior of the angles
What is the measure of an inscribed angle
Half the measure of its intercepted arc
Two inscribed angles that intercept the same arc are
Congruent
An angle inscribed in a semicircle is a
Right angle
The opposite angles of a quadrilateral inscribed in a circle
Are supplementary
The measure formed by a tangent and a chord is
Half the measure of an intercepted arc
Define Secant
A line that intersects a circle at two points
The measure of an angle formed by two lines that intersect in a circle is
Half the sum of the measures of the intercepted arcs
The measure of an angle formed by two lines that intersect outside a circle is
Half the difference of the measures of the intercepted arcs
An equation of a circle with the center ( h,k) and radius is
(X-h) squared + (y-k) squared = the radius squared
