Geometry Circles & Arcs 2

Question 1

A central angle measures 72°. What fraction of the full circle does its arc represent?

Accepted Answer

1/5

Answer

72° ÷ 360° = 1/5 of the circle.

Question 2

An inscribed angle intercepts an arc of 100°. What is the measure of the inscribed angle?

Accepted Answer

50°

Answer

An inscribed angle is half its intercepted arc, so 100° ÷ 2 = 50°.

Question 3

A circle has radius 6. What is the length of an arc subtended by a central angle of 60°?

Accepted Answer

2π

Answer

Arc length = (60/360) × 2π(6) = (1/6)(12π) = 2π.

Question 4

Two tangents drawn from an external point to a circle are always:

Accepted Answer

Equal in length

Answer

Tangent segments from a common external point are congruent.

Question 5

A sector has a central angle of 90° in a circle of radius 4. What is its area?

Accepted Answer

4π

Answer

Sector area = (90/360) × π(4²) = (1/4)(16π) = 4π.

Geometry Practice Test