Circle Theorems-“No Brainers”
1. Central Angle
C
Equals the arc
O
B
D
2. Inscribed Angle
C
B
Equals ½ the arc
O
D
3. Diameter ┴ Chord
A
C
E
O
B
D
BISECTED chords & arcs
Right <‘s formed
C
4. Angles formed by 2 chords
B
E
D
Arc  Arc
2
A
5. Segments formed by 2 chords
C
B
E
POP = POP
D
A
6. Angle formed by Chord and Tangent
B
(CE)(ED)=(AE)(BE)
A
Equals ½ the arc
O
C
7. Angle formed by 2 secants
P
R
O
Q
T
S
BigArc  SmallArc
2
8. Segments formed by 2 secants
W
R
O
O
T
S
W
O
P
Q
WO = WO
(whole)(outter)
9. Angle formed by a tangent & a secant
P
O
Q
R
S
BigArc  SmallArc
2
10. Segments formed by a tangent & a secant
P
O
Q
R
S
T² = WO
Tangent² =(whole)(outter)
11. Radius and Tangent
A
C
O
Perpendicular…
right <‘s are formed
B
12. Angle formed by 2 tangents
P
(360-x)
R
x
O
BigArc  SmallArc
2
Q
S
13. Segments formed by 2 tangents
P
R
Q
O
S
Are equal…
”Clown Hat” Theorem
congruent arcs.
14.Congruent chords have _____________
360º degrees.
15.A circle has _________
congruent arcs.
16.Parallel lines intercept _____________
180º
17. A diameter creates 2 arcs of _________.
180º
d
2 radius
18. A diameter = ___
r
r
180º
Circle Theorems used in Proofs
1. All diameters or radii of a circle are congruent.
2. Congruent chords intercept congruent arcs.
Congruent arcs are intercepted by congruent chords.
3. Parallel chords intercept congruent arcs.
4. A tangent is perpendicular to a radius at the point of tangency.
5. Tangents drawn to a circle from the same exterior point are
congruent.
6. Congruent central angles intercept congruent arcs.
Congruent arcs are intercepted by congruent central angles.
7. Angles inscribed to the SAME arc are congruent.
8. Angles inscribed to CONGRUENT arcs are congruent.
9. An angle inscribed in a semi-circle is a right angle.
10. A triangle inscribed in a semi-circle is a right triangle.
11. Two circles with congruent radii or congruent diameters are
congruent.