Circles, Chords, and Central Angles

Circles Prereq

Parts of a Circle

Central and Inscribed Angles

• Central angles are created by two radiis meeting at the center of circle

• Central angles are EQUAL to their intercepted arc.

• Inscribed angles are created by two chords meeting ON the perimeter of the circle.

• Inscribed angles are half the measure of the intercepted arc.

Multiple Choice

• a
• b
• c
• d

Multiple Choice

Determine the measure of Arc BA.

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• Inscribed Angle
• Central Angle 

Multiple Choice

• Secant
• Diameter
• Tangent
• Chord

Multiple Choice

Which line segment represents the diameter of the circle?

• PQ
• AO
• AB
• OC

Multiple Choice

Which is the name of this part of the circle?

• SEMI CIRCLE

• ARC

• RADIUS

• CHORD

Multiple Choice

Which is the name of this part of the circle?

• CIRCUMFERENCE

• DIAMETER

• CHORD

• SEGMENT

Interior Angles

• Interior angles are created by two chords or secants that intersect within a circle

• The angle is is equal to the average of the intercepting arcs

• EX: angle 3 is equal to 1/2(arc QP+arc RS) **angles 1 and 3 are equivalent

• EX: angle 4 is equal to 1/2(arc PS+ arc QR)

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Angle Inside Circle

• A
• B
• C
• D

Exterior Angles

• Exterior angles are created by two secants and or tangents

• Exterior angles are equal to half the difference of the intercepting arcs

• EX: angle 2 is equal to 1/2(arc RS-arc RQ)

• EX: angle 3 is equal to 1/2(arc BJH - arc BH)

Multiple Choice

Given a tangent and a secant, solve for x.

• 135°
• 150°
• 160°
• 180°

Multiple Choice

Determine the measure of arc CD.

• 64°
• 84°
• 104°
• 114°

Multiple Choice

Given two secants, solve for x.

• 40°
• 70°
• 110°
• 150°

Segment lengths

• https://youtu.be/ASZl3SnKwI8

• Check out the video

Multiple Choice

Solve for x. 

• 7.94
• 8
• 10.58
• 112

Multiple Choice

Solve for x. Assume that lines which appear tangent are tangent.

• 11

• 17

• 18

• 12

Multiple Choice

Find the length of WU

• 5

• 18

• 3

• 11

Multiple Choice

Assume that all the lines that appear tangent are tangent. Find the perimeter

• 54
• 36
• 48
• 42

Multiple Choice

QS is a tangent to circle P. Find QS.

• 144

• 14

• 12

• 13

Area of a Sector and Arc Length

• The arc length is a part of the circumference. (See the formula on the right)

• The area of a sector is a part of the total area. (See the formula on the right)

Multiple Choice

What is the area of sector​ GPH?

• 9π yd²

• 32π yd²

• 18π yd²

• 6π yd²

Multiple Choice

Find the length of the bold arc.Leave pi in your answer.

• 5688π ft
• 15.8π ft
• 150.4π ft
• 54,150 ft

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47
• 74
• 94
• 123

Multiple Choice

Find the area of the sector, rounding your answer to 1d.p.

• 67.1cm²

• 67.0cm²

• 16.8cm²

• 134.0cm²