Section 1.6 – Circles Vocabulary • Circle – the set of all points in a plane at a given

distance (radius) from a given point (center) in the plane. You name a circle by its center.

• Radius – a segment from the center to a point on the circle. The radius is half the length of the diameter

• Diameter – a line segment containing the center with its endpoints on the circle. The diameter is twice the length of the radius.

• Congruent circles – circles are congruent if their radii are the same length.

• Concentric circles – circles that share the same center point.

• Arc of a circle – the two points on the circle and the continuous (unbroken) part of the circle between the two points.

• Endpoints of an arc – the two points are the endpoints of the arc.

• Semicircle – an arc of a circle whose endpoints are the endpoints of a diameter. Semicircles need to be named with three points.

Chapter 6 – Circle Vocabulary• Minor arc – an arc of a

circle that is smaller than a semicircle. Minor arcs can be named with two points.

• Major arc – an arc of a circle that is larger than a semicircle. Major arcs must be named with three points.

This is called arc AB and iswritten AB

B

A

C

This is called arc ACB and

is written ACB

BA

• Arc measures – arc measures are found by measuring the corresponding central angle. The MEASURE of an arc is always in degrees.

• Arc Lengths – are found by calculating the length of the portion of the circumference that is the arc. The LENGTH of an arc is always measured in units.

mABC = 90.59

That means that mAC = 90.59

BA

C

If the radius of the circle above is 15, then you would do the following calculation to find the length of the arc:

degree 90.592 2 15360 360

r

• Central angle – the angle with its vertex at the center of the circle and sides passing though the endpoints of the arc.

• Inscribed angle – an angle whose vertex is on the circle and intercepts an arc of the circle

ABC is acentral angle

B

A

C

DADC is aninscribed angle andit intercepts AC

A

C

• Chord – a chord is a line segment whose endpoints lie on the circle. A diameter is a chord that goes through the center of the circle.

• Tangent – a tangent is a line that intersects the circle only once.

• Point of Tangency – the point where the tangent touches the circle.

K

A

AK is a chord.

TH is tangent to circle M at point T

M

H

T

• Tangent circles – are two circles that are tangent to the same line at the same point.

• Internally tangent – are tangent circles where one circle is inside the other circle.

• Externally tangent – are tangent circles where both circles are on opposite sides of the tangent line (we say the circles are external to each other).

R

Circles T and M are internally tangent.

M

H

T

R

Circles T and G are externally tangent.G

H

T

• Cyclic Quadrilateral – a quadrilateral that is inscribed in a circle.

• Secant – a line that intersects a circle at two points.

• Circumference – the perimeter of a circle or the distance around a circle. The formula for the circumference of a circle is 2*Pi*r or Pi*d.

ABCD is a cyclic quadrilateral

C

A

B

D

AB is a secant

B

A