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˚