Worksheet: Identify Tangents and Using Its Properties

A tangent is a line in the same plane as a circle that intersects it. This worksheet assesses your ability to identify a common tangent and how to use the properties of tangents to find missing values.

Q1:

What is the name of a line that meets a circle in exactly one point?

Asegment
Barc
Ctangent
Dradius
Echord

Q2:

If two circle intersect at two points, how many common tangents do they have?

Q3:

If I draw two tangent segments from a point outside the circle, are they equal in length?

Ayes
Bno

Q4:

If two circles lie outside each other, how many common tangents do they have?

Q5:

If I draw two tangents to a circle, one from each end of a diameter, are the tangents parallel?

Ayes
Bno

Q6:

Given that and are two tangent segments to a circle at the points and , and , determine the length of .

Q7:

Find the value of .

Q8:

In the figure, line is tangent to the circle at . What is the length ?

Q9:

Given that touches the circle at , , and . Find the length of , and approximate the result to the nearest tenth.

Q10:

Given that is a tangent to the circle , find the length of .

Q11:

Suppose that, in the figure, is tangent to the circle at , , and . What is the length of ?

A32 cm
B76.8 cm
C51.2 cm
D83.2 cm

Q12:

In the figure, is tangent to circle at , meets the circle at , , and . Find the circle’s diameter to the nearest tenth.

Q13:

Circle has radius 11 cm. If , what is ? Answer to the nearest tenth.

Q14:

Line is tangent to circle at . Given that , , what is ?

Q15:

Line is tangent to circle at . Given that , , what is ?

Q16:

Given that , find and to the nearest thousandth, if needed.

Q17:

The two circles and are touching externally. is a common tangent to them at and respectively, is a common tangent to them at and respectively. Given that , and , find and .