Geometry Circles & Arcs 3

Question 1

A chord is 8 units long and is 3 units from the center. What is the radius (to nearest whole)?

Accepted Answer

5

Answer

Half-chord 4, distance 3: r = √(4² + 3²) = √25 = 5.

Question 2

Two chords intersect inside a circle. One is divided into segments 3 and 8; the other into 4 and x. Find x.

Accepted Answer

6

Answer

By the intersecting chords rule, 3×8 = 4×x, so x = 24/4 = 6.

Question 3

The circumference of a circle is 31.4. Using π ≈ 3.14, what is the diameter?

Accepted Answer

10

Answer

C = πd, so d = 31.4 / 3.14 = 10.

Question 4

A tangent line meets a radius at the point of tangency at an angle of:

Accepted Answer

90°

Answer

A radius is always perpendicular to a tangent at the point of contact.

Question 5

The arc opposite a 40° inscribed angle measures:

Accepted Answer

80°

Answer

The intercepted arc is twice the inscribed angle: 2 × 40° = 80°.

Geometry Practice Test