# Lesson Worksheet: Tangents of a Circle Mathematics

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

**Q2: **

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

- Atangent
- Bsegment
- Cchord
- Darc
- Eradius

**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 .

**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 of center , 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 .

**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,