Post on 01-Jan-2016
description
Circles
THEIR
PARTS
AND
Radius
D
I
A
M
E
T
E
R
CHORD
TANGENT
Tangent lines intersecting a diameter or radii at the point of tangency are
perpendicular
A line outside the circle and touching the circle at one
point.
CENTRAL ANGLES
Central Angles- angles whose vertex is at the center of the circle
1200
The intercepted arc of a central angle is equal to
the measure of the central angle
A
B
C
ARC AB = 1200
Inscribed Angle
An inscribed angle is an angle with its vertex ”on” the circle, formed by two
intersecting chords
A
B
CO
Inscribed angle = ½ intercepted Arc
100o
<ABC is an inscribed angle. Its intercepted arc is minor arc from
A to C, therefore
m<ABC = 500
Inscribed Quadrilateral
• A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary
70˚
120˚
40˚
140˚
A Triangle inscribed in a circle
• A triangle inscribed in a semi-circle , having a hypotenuse as a diameter is a right triangle.
30˚
60˚
P
Tangent Chord Angle
B
C
A
120o
An angle formed by an intersecting tangent and chord
with the vertex “on “ the circle.
Tangent Chord Angle = ½ intercepted arc
<ABC is an angle formed by a tangent and chord. Its intercepted arc is the
minor arc from A to B, therefore m<ABC = 60o
Angles formed by intersecting chords (not
diameters)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=
½ sum of the intercepted arcs
80
5060
170
A B
CD
m< AEB = ½(80 +170) = 1/(250) = 125
E
Angle Formed Outside of a Circle by the Intersection of:
• “Two Tangents”A
B
C
D
2100
150o
The angle is ½ of the difference of the two arcs formed by the
tangents.>ABC = ½(210 – 150) =
30˚
• “Two Secants”
A
B
C
D
E
95o
20o
An angle formed by two secant on the
outside of the circle .The measure of the
angle is ½ the difference of the intersected arcs.
<ACB = ½(95 – 20) = 37.5˚