1. Circle Theorems-“No Brainers”
1. Central Angle
Equals the arc
2. Inscribed Angle
Equals ½ the arc
3. Diameter ┴ Chord
BISECTED chords & arcs
Right <‘s formed

2. (CE)(ED)=(AE)(BE) 4. Angles formed by 2 chords
5. Segments formed by 2 chords
POP = POP
(CE)(ED)=(AE)(BE)
6. Angle formed by Chord and Tangent
Equals ½ the arc

3. W W 7. Angle formed by 2 secants 8. Segments formed by 2 secants O O
WO = WO
(whole)(outter) W

4. Tangent² =(whole)(outter)
9. Angle formed by a tangent & a secant
10. Segments formed by a tangent & a secant T² O
T² = WO
Tangent² =(whole)(outter) W

5. right <‘s are formed
11. Radius and Tangent
Perpendicular…
right <‘s are formed
12. Angle formed by 2 tangents
(360-x) x
13. Segments formed by 2 tangents
Are equal…
”Clown Hat” Theorem

6. r congruent 360º congruent 180º 180º 2 180º
Congruent chords have _____________ arcs.
A circle has _________ degrees.
Parallel lines intercept _____________ arcs.
17. A diameter creates 2 arcs of _________.
360º
congruent
180º
180º d 2
18. A diameter = ___ radius r
180º

7. Circle Theorems used in Proofs
All diameters or radii of a circle are congruent.
Congruent chords intercept congruent arcs.
Congruent arcs are intercepted by congruent chords.
Parallel chords intercept congruent arcs.
A tangent is perpendicular to a radius at the point of tangency.
Tangents drawn to a circle from the same exterior point are congruent.
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.
Two circles with congruent radii or congruent diameters are congruent.