# Worksheet: Tangents of a Circle

In this worksheet, we will practice using the properties of tangents of circles to find missing angles or side lengths.

Q1:

Given that is a tangent to the circle at , and , find . Q2:

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

• Atangent
• Bsegment
• Cchord
• Darc

Q3:

Circle has radius 11 cm. If , what is ? Answer to the nearest tenth. Q4:

Given that , find and to the nearest thousandth. • A,
• B,
• C,
• D,

Q5:

Given that is a tangent to the circle , and , determine . Q6:

Given that is tangent to the circle at , , and , find the length of , and round the result to the nearest tenth. Q7:

In the figure below, circle, , , , and is a tangent, find the perimeter of the figure . Q8:

Given that is a tangent to the circle and , find . Q9:

Given that is a tangent to the circle , and , determine . Q10:

Given that is a tangent to the circle at , , and is the midpoint of , find . Q11:

Given that , find the length of rounding the result to the nearest hundredth. Q12:

Given that is a tangent to the circle at , , , and , determine the perimeter of . Q13:

Given that is a tangent to the circle , Find the perimeter of . Q14:

Suppose that, in the figure, is tangent to the circle at , , and . What is the length of ? Q15:

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

Q16:

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

• Ayes
• Bno

Q17:

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

Q18:

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

• Ayes
• Bno

Q19:

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

Q20:

Find the value of . Q21:

In the figure, line is tangent to the circle at . What is the length ? Q22:

Given that is a tangent to the circle , find the length of . Q23:

In the figure, is tangent to circle at , meets the circle at , , and . Find the circle’s diameter to the nearest tenth. Q24:

Line is tangent to circle at . Given that , , what is ? Q25:

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 . • A,
• B,
• C,
• D,