Unit 8 - Circle Theorems Flashcards
(28 cards)
What is the theorem when you want to prove that chords of central angles are congruent if central angles are congruent
In a circle or congruent circles, congruent central angles create congruent chords
What is the theorem you use when you have congruent chords and you want to prove that their central angles are congruent
In a circle or congruent circles, congruent chords have congruent central angles
What is the theorem you use when you have congruent arcs and you want to prove that their chords are congruent
In a circle or in congruent circles, if arcs are congruent, then the chords that cut them off are congruent
What is the theorem you use when you have congruent chords but you want to prove that their arcs are congruent
In a circle or in congruent circles, if chords are congruent, then they cut off congruent arcs
What is the definition and the formula of the central angle
an angle whose vertex is the center of a circle
m<) ABC = arc mAC
What is the definition and formula for an inscribed angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
m<)ABC = 1/2 arcAC
Definition and formula of central angle
An angle whose vertex is the center of a circle
m<)ABC = arc mAC
Definition and formula of Inscribed Angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
m<)ABC = 1/2 arc mAC
Definition and formula of Chords intersecting inside a circle
Chord: A segment whose endpoints are on a circle
m<)AEC = m<)bed = 1/2 (arc mAC + arc mDB)
Intersecting Chords Inside a circle equality theorem
(a)(b) = (c)(d)
Tangent to Tangent from an external point formula
AB = AC
Secant to Secant from external point
(outside)(whole) = (outside)(whole)
Secant to Tangent from an external point
(Tangent) squared = (outside)(whole)
Tangent Chord formula and definition
Tangent: A line, segment, or ray that intersects a circle at one point
m<)ACE = 1/2 arc mABC
Tangent Tangent external angle and arc theorem
m<)D = 1/2 (arc mABC - arc mAC)
Secant Secant external angle and arc theorem
m<)C = 1/2 (arc mAE - arc BD)
Secant Tangent external angle and arc theorem
m<)B = 1/2 (arc AD - arc AC)
Theorem for an angle inscribed in a semicircle
An angle inscribed in a semicircle is a right angle
Theorem for inscribed angles that intercept the same arc
In a circle, inscribed angles that intercept the same arc or congruent arcs are congruent
Theorem for when parallel lines cut off an arc
Parallel lines cut off congruent arcs of a circle
Theorem for when the measure formed by a tangent and a chord
The measure of an angle formed by a tangent and a chord is 1/2 the measure of its intercepted arc
Theorem for opposite angles in a quadrilateral if its inscribed in a circle
If a quadrilateral is inscribed in a circle, opposite angles are supplementary
Definition and formula of Arc Length
An arc length is a portion of the circumference of a circle. It is measured in a unit of distance. In a circle, the ratio of the length of a given arc to the circumference of the circle is equal to the ratio of the measure of the arc to 360 degrees
arc of length of AB arc mAB
____________________ = ________
2PIr 360 degrees
arc of length of AB over 2PIr = arc mAB over 360
