|
1. Central Angle:
A central angle is an angle formed by two intersecting radii such that
its vertex is at the center of the circle.
|
Central Angle = Intercepted Arc |
<AOB is a central angle.
Its intercepted arc is
the minor arc from
A to B. m<AOB = 80º
|
 |
|
|
2. Inscribed Angle:
An inscribed angle is an angle with its vertex "on" the circle, formed by two
intersecting chords.
|
Inscribed Angle =
 Intercepted
Arc |
<ABC is an inscribed angle.
Its
intercepted arc is the minor arc from A to C.
m<ABC = 50º |
|
|
|
3. Tangent Chord Angle:
An angle formed by an intersecting tangent and chord has its vertex "on" the circle.
|
Tangent Chord
Angle =
Intercepted
Arc |
<ABC is an angle formed by a tangent and chord.
Its intercepted
arc is the minor arc from A to B.
m<ABC = 60º
|
 |
|
|
4. Angle Formed Inside of a
Circle by Two
Intersecting Chords:
When two chords intersect "inside" a circle, four angles
are formed. At the point of intersection, two sets of vertical
angles can be seen in the corners of the X that is formed on the
picture. Remember: vertical angles are equal.
|
Angle
Formed Inside by Two
Chords =
Sum
of Intercepted Arcs |
|
Once you have found ONE of these angles, you
automatically know the sizes of the other three by using your
knowledge of vertical angles (being equal) and adjacent angles forming
a straight line (adding to 180). |
|
<BED is formed by two intersecting chords.
Its
intercepted arcs are
 .
[Note: the intercepted arcs belong to the set of vertical
angles.]
also, m<CEA = 120º (vetical angle)
m<BEC and m<DEA = 60º by straight line.
|
|
|
5. Angle Formed Outside of a
Circle by the Intersection of:
"Two Tangents" or "Two Secants"
or "a Tangent and a Secant".
|
The formulas for all THREE of these
situations are the same:
Angle Formed Outside = Difference
of Intercepted Arcs
(When subtracting, start with the larger
arc.) |
|
|
Two Tangents:
<ABC is formed by two tangents intersecting outside of circle O.
The intercepted arcs are minor arc AC and major arc AC.
These two arcs together comprise the entire circle.
|
 |
|
Special situation for
this set up: It can be proven that <ABC and
central <AOC are supplementary. Thus the angle formed by
the two tangents and its first intercepted arc also add to 180º. |
|
|
|
Two Secants:
<ACE is formed by two secants intersecting outside of circle O.
The intercepted arcs are minor arcs BD and AE.
|
 |
|
|
a Tangent and a Secant:
<ABD is formed by a tangent and a secant intersecting outside of circle O.
The intercepted arcs are minor arcs AC and AD.
|
 |
|
