Mastering Circle Theorems

What is the angle subtended at the center of a circle by an arc?

• The angle subtended at the center of a circle by an arc is equal to the angle formed by the two radii connecting the endpoints of the arc.

• The angle is determined by the circumference of the circle.

• The angle subtended at the center is always 90 degrees.

• The angle is equal to the length of the arc divided by the radius.

Identify the theorem that states the angle at the circumference is half the angle at the center.

• The Angle at the Center Theorem

• The Exterior Angle Theorem

• The Central Angle Theorem

• The Inscribed Angle Theorem

Calculate the length of an arc with a radius of 10 cm and a central angle of 60 degrees.

• 10.47 cm

• 20.00 cm

• 15.71 cm

• 5.24 cm

What is the relationship between the angles formed by two chords that intersect inside a circle?

• The angles are equal to the sum of the measures of the intercepted arcs.

• The angles are equal to the measures of the chords that intersect.

• The angles are equal to half the sum of the measures of the intercepted arcs.

• The angles are equal to the difference of the measures of the intercepted arcs.

Determine the length of a chord in a circle with a radius of 8 cm that subtends a central angle of 90 degrees.

• 8√2 cm

• 4√2 cm

• 16 cm

• 8 cm

Explain the relationship between the angles formed by a tangent and a chord.

• The angle formed by a tangent is independent of the chord.

• The angle between a tangent and a chord is always 90 degrees.

• The angle between a tangent and a chord is equal to the angle subtended by the tangent at the center.

• The angle between a tangent and a chord is equal to the angle subtended by the chord at the opposite arc.

If two chords intersect inside a circle, how do you calculate the angles formed?

• Angle = Arc1 + Arc2

• Angle = 1/2 (Arc1 + Arc2)

• Angle = Arc1 - Arc2

• Angle = 1/2 (Arc1 - Arc2)

What is the theorem that states that the angle between a tangent and a chord is equal to the angle in the alternate segment?

• Alternate Segment Theorem

• Segment Angle Theorem

• Chord Angle Theorem

• Tangent-Chord Theorem

Calculate the arc length of a circle with a radius of 5 m and a central angle of 120 degrees.

• 7.85 m

• 15.71 m

• 5.24 m

• 10.47 m

Identify the properties of equal chords in a circle.

• Equal chords are of the same length, equidistant from the center, and subtend equal angles at the center.

• Equal chords do not subtend any angles at the center.

• Equal chords are located at different distances from the center.

• Equal chords are always longer than unequal chords.