# Worksheet: Special Segments in a Circle

In this worksheet, we will practice using the theorems of intersecting chords, secants, or tangents and secants to find missing lengths in a circle.

**Q2: **

Given that , , , and , do the points , , , and lie on a circle?

- Ayes
- Bno

**Q5: **

Points , , and , , are collinear. Suppose that , , , and . Do points , , , and lie on a circle?

- Ano
- Byes

**Q6: **

What is the radius of circle ?

**Q10: **

Given that , , , and , do the points , , , and lie on a circle?

- Ano
- Byes

**Q11: **

Points , , and , , are collinear. Suppose that , , , and . Do points , , , and lie on a circle?

- Ano
- Byes

**Q12: **

and are two chords of a circle of center and radius 26. Suppose that is perpendicular to both and and contains a point with . Find the lengths of and .

- A ,
- B ,
- C ,
- D ,

**Q13: **

If , , and , find the lengths of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q14: **

A circle has center and radius 13 cm. A line passes through the points , , and where and are on the circle, is 25 cm from the point , and . Calculate the length of and the perpendicular distance between the line and the point . Round your answers to 2 decimal places.

- A ,
- B ,
- C ,
- D ,

**Q16: **

In the figure shown, the circle has a radius of 12 cm, , and . Determine the distance from to the center of the circle, , and the length of , rounding your answers to the nearest tenth.

- A 19.6 cm, 20.2 cm
- B 3.4 cm, 26.6 cm
- C 3.4 cm, 20.5 cm
- D 11.5 cm, 20.2 cm

**Q17: **

In the figure below, is a diameter of the circle , , , , and . Find the length of .

**Q19: **

Are the points , , , and lying on a circle?

- Ano
- Byes

**Q20: **

Given that , , , and , find the value of .

- A
- B
- C
- D

**Q21: **

Given that the circle shown below has a radius of 25 cm, , and , find the length of .

- A14 cm
- B30 cm
- C cm
- D25 cm

**Q22: **

and are two chords of a circle intersecting at . Find , where , , and .

- A2
- B20
- C5
- D12.8
- E5.6

**Q23: **

and are two intersecting line segments at inside a circle, where , , , and . Are and chords?

- AYes
- BNo

**Q24: **

In the given figure, , , and . Find the length of .

**Q25: **

Find the value of .