Circle Angle Measures and Segments

A _________ is a segment in a circle that has endpoints on the circle.

• Radius

• Diameter

• Chord

• Arc

A __________ is the longest chord in a circle and goes through the center of a circle.

• Diameter

• Arc

• Chord

• Radius

Identify all radii.

If the circumference of a circle is 40π cm, what is the length of its radius.

• 20 cm

• 40 cm

• 80 cm

• 20π cm

Find the length of the highlighted arc.

Angle PTQ is a _______ angle.

What is the measure of ∠PTQ?

• 100°
• 140°
• 180°
• 120°

Answer explanation

The sum of the measures of the arcs of a circle is 360^o.

120 + 60 + 40 + x = 360

Solve for x. 

• 5
• 20
• 40
• 85

Answer explanation

The measure of an arc is equal to the measure of the central angle that intercepts it.

4x + 5 = 85

Find the value of x.

• 10
• 181
• 34
• 40

Answer explanation

Chords that are equidistant from the center of a circle are congruent. So, the length of chord AB equals the length of chord DC.

3x - 11 = x + 9

CM = 6x + 1 and ME = 8x - 5. Find CE.

• 19

• 3

• 38

• 18.8

Answer explanation

When a diameter is perpendicular to a chord of a circle, it bisects that chord.

6x + 1 = 8x - 5

Find x, then find the sum of CM and ME.