Tangents and Circles

Find the measure of the missing arc.

• 70°

• 100.5°

• 201°

• 140°

Find the value of x

• 10

• 15

• 12

• 19

If a line intersects a circle at exactly one point, it is called a:

• Chord

• Diameter

• Secant

• Tangent

What is the angle between a tangent to a circle and the radius drawn to the point of contact?

• 45 degrees

• 90 degrees

• 180 degrees

• 0 degrees

If two tangents are drawn to a circle from an external point, then the lengths of these tangents are:

• Not necessarily equal

• Always equal

• Inversely proportional to the radius

• Directly proportional to the radius

What can be said about the tangents drawn from an external point to a circle?

• They subtend equal angles at the center

• They are perpendicular to each other

• They subtend equal angles at the point of contact

• They are parallel to each other

If a tangent at point P and a diameter AB of a circle intersect at the point P, which statement is true?

• ∠APB = 90 degrees

• ∠APB = 45 degrees

• ∠APB = 180 degrees

• ∠APB = 0 degrees

If a tangent at point P and a chord AB of a circle intersect at the point P, which statement is true?

• ∠APB = 90 degrees

• ∠APB = 45 degrees

• ∠APB = 180 degrees

• ∠APB = 0 degrees

In a right-angled triangle, if one side is a radius and the hypotenuse is a tangent to the circle, what is the angle opposite to the radius?

• 45 degrees

• 90 degrees

• 30 degrees

• 60 degrees

Find the value of x

• 4

• 18

• 3

• 9