Geometry Circles & Arcs 5

Question 1

Two secants from an external point intercept arcs of 120° and 40°. The angle between the secants is:

Accepted Answer

40°

Answer

External angle = half the difference: (120° − 40°)/2 = 40°.

Question 2

A circle is inscribed in a square of side 10. The circle's radius is:

Accepted Answer

5

Answer

The inscribed circle's diameter equals the side (10), so radius = 5.

Question 3

The measure of a tangent-chord angle equals:

Accepted Answer

Half the intercepted arc

Answer

A tangent-chord angle equals half its intercepted arc.

Question 4

A circle of radius 5 has a sector with arc length 5π. Its central angle is:

Accepted Answer

180°

Answer

Circumference is 10π; 5π is half, so the angle is 180°.

Question 5

Point P is 13 units from the center of a circle with radius 5. The tangent length from P is:

Accepted Answer

12

Answer

Tangent = √(13² − 5²) = √144 = 12.

Geometry Practice Test