# Worksheet: Relations between Arcs, Chords, and Diameters

In this worksheet, we will practice identifying arcs, chords, and diameters and using the relations between them to solve problems.

**Q1: **

Which segment in this circle is a chord?

- A
- B
- C

**Q3: **

Points and are midpoints of segments and respectively. If , what is ?

**Q4: **

The radius of the circle below is 87 cm, , and is the midpoint of . Given that intersects at and , find the length of .

**Q6: **

Given and , find .

**Q7: **

In circle , suppose and . Find the lengths of and to the nearest hundredth.

- A11.43, 11.00
- B22.00, 1.60
- C11.43, 1.60
- D5.71, 11.00

**Q8: **

In the given circle, cm and cm. Determine the lengths of and .

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

**Q9: **

In the following figure, determine all the chords of the circle.

- A
- B
- C
- D

**Q10: **

The distance between the two lines and is 13 and . If the radius of the circle is 10.5, what is the length of ? Round your answer to two decimal places.

**Q11: **

Given that , and cm, determine the length of .

**Q12: **

Given that , , , and , determine the value of and the length of .

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

**Q13: **

Given that , , and , find the length of .

**Q14: **

In the circle , if , find the length of .

**Q15: **

In circle , . Find .

**Q16: **

If , what is ?

**Q17: **

The radius of circle is 60.9 cm, and . What is the area of ?

**Q18: **

In the figure, the two circles are concentric at and . Calculate the area of the shaded region, to the nearest hundredth.

**Q19: **

Two circles have been cut out of the bigger circle as seen in the picture. The point lies on both of the smaller circles and is the center of the larger circle.

Work out the remaining area. Give your answer accurate to two decimal places.

**Q20: **

Two small circles with the same diameter are drawn inside a larger circle as shown. Given that the diameter of the large circle is 9.8 mm, determine, to the nearest tenth, the area of the shaded part.

**Q21: **

The circumference of circle is 36.6 cm. Calculate to the nearest tenth.

**Q22: **

In the figure, the smaller of the concentric circles is tangent to chord at . If the large circle has radius 67 cm, and , what is the radius of the smaller circle?

**Q23: **

If , find the range of values of that satisfies the data represented.

- A
- B
- C
- D

**Q24: **

Point is at a distance 13 from , which is the center of a circle of radius 7.3. Draw ray to intersect the circle at and , with between and . If , what is ?

**Q25: **

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

- A 25 cm
- B cm
- C 14 cm
- D 30 cm