Central Angles and Arcs of Circles Graphic Organizer

Central Angles and Arcs of Circles Graphic Organizer

Vocabulary Word / Definition / Example
Circle / The planer group of points that are the same distance from a common point, called the center
Center / The center of the circle, the point all the radii start from / Point O
Radius / The distance from the center to a point on the edge / ON
Chord / A line segment with both ends on the edge of the circle / ND
Diameter / A chord that includes the center / AC
Secant / A line that intersects the circle at two points / FH
Tangent / A line that intersects the circle at one point / KL
Point of
Tangency / The point the radius and tangent line share. The radius and tangent line are perpendicular at the point of tangency / Point B
Central Angle / An angle whose vertex is at the center of the circle / ÐNOA
Inscribed Angle / An angle whose vertex is on the circle / ÐNDA
Semicircle / Exactly one-half of the circle, named by 3 points / ADC
Arc / Any unbroken part of the circumference of the circle, named by its endpoints / AD
Minor Arc / Smallest arc formed by a secant and a circle – named by the end points and one intermediate point / AD
Major Arc / Largest arc formed by a secant and a circle. It goes more than halfway around the circle, named using points / NBC
Congruent Circles / Circles with the same radius
Congruent Arcs / Arcs with the same central angle
Arc Length / Length of circumference between two points on the circle
Measure of Arc / Equal to the measure of the central angle

Chord, Secant, Tangent Angles in Circles

Central Angle
Vertex is _center of__ 8 / Mathematical Statement:
The measure of the central angle equals the measure of the intersected arc.
m ÐBAC = m arc BC
Calculations: /
Inscribed Angle
Vertex is __ON the__ 8 / Mathematical Statement:
The measure of an inscribed angle equals half the measure of the intercepted arc
mÐBDC = ½ mÐBAC
mÐBDC = ½ m arc BC
Calculations: /
Two Inscribed Angles, same arc
Vertex is __On the_ 8 / Mathematical Statement:
Inscribed angles intersecting the same arc are congruent
mÐBCE = mÐBDE
Calculations: /
Inscribed Angle
Vertex is ON the_8 / Mathematical Statement:
The measure of an inscribed angle intersecting a diameter or semi circle equals 90°
m Ð ABC = 90°
Calculations: /
Inscribed Angle
Vertex is __On the_ 8 / Mathematical Statement:
The measure of an inscribed angle equals half the measure of the intercepted arc
mÐCDE = ½ m arc CBE
Calculations: /
Inscribed Quadrilateral
Vertex is _On the 8 / Mathematical Statement:
Opposite angles of a quadrilateral inscribed in a circle are supplementary
mÐCBE + mÐCDE = 180°
mÐBCD + mÐBED = 180°
Calculations: /
Two Chords
Vertex is _Inside the 8 / Mathematical Statement:
The measure of the angle formed by two chords equals half the sum of the intercepted arcs of the vertical angles formed
mÐUWV = ½ (m arc ST + m arc UV)
Calculations: /
Two Secants
Vertex is _Outside_ 8 / Mathematical Statement:
m Ð CAD = ½ (m arc CD – m arc BE)
Calculations: /
Secant/Tangent
Vertex is _Outside 8 / Mathematical Statement:
m ÐEDG = ½ (m arc EG – m arc EF)
Calculations: /
Tangent/Tangent
Vertex is _Outside the 8 / Mathematical Statement:
mÐBAC = ½ (m major arc – m minor arc)
Calculations: /

Chords of Circles Theorem Graphic Organizer

Chords in Circles Theorem # 1

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
_BC_ @ __DE__ if and only if __BC__ @ __DE__ /

Chords of Circles Theorem #2

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
If diameter __GK_ ^ ____HI_, then
_HJ__ @ __JI_ and _HK__ @ _KI__ /

Chords of Circles Theorem #3

If one chord is perpendicular bisector of another chord, then the first chord is a diameter.
If chord __QT_ is ^ to _SR_ and _SJ___ @ _JR__,
then _QT__ is a diameter of the circle /

Chords of Circles Theorem #4

In the same circle, or in congruent circles, two chords are congruent if and only if they are the same distance from the center.
_DE__ @ _CB_ if and only if _FA___ @ __AG___ /

Chord, Secant, Tangent Lengths in Circles

Two Chords
Vertex is __Inside the_ 8 / Mathematical Statement:
The product of the parts are equal
SW * WU = TW * WV
Calculations: /
Two Secants
Vertex is _Outsid the __ 8 / Mathematical Statement:
Outside * Whole = Outside * Whole
OW = OW
AB * AC = AE * AD
Calculations: /
Secant/Tangent
Vertex is Outsid the_8 / Mathematical Statement:
ED2 = DF * DG
Calculations: /
Tangent/Tangent
Vertex is Outside the 8 / Mathematical Statement:
AB = AC
Calculations: /