In this worksheet, we will practice solving word problems involving the equation of a circle.

**Q4: **

Three street lights are on the border of a circular park. If three street lights can be modeled by the points , , and , write the equation of the circle that would model the park.

- A
- B
- C
- D
- E

**Q5: **

Given that , , and are the centres of three circles whose radii are 8, 10, and 5 length units, respectively, and that length units, find the general form of the equations of circles and .

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

**Q6: **

The given figure shows a pulley having a radius of 5 units, and touching the two coordinate axes. It is operated by a wire that passes over a smaller pulley . If the equation of circle of pulley is , and each unit of the coordinate axes represents 4 cm, determine the distance between the centres of the two pulleys.

**Q7: **

A building is in the shape of a regular octagon. Given that the vertices of the octagon lie on the circle , what is the area of the building to the nearest square unit?

**Q8: **

The figure below represents a vertical cross-section of a tunnel, where the equation of its circle is , and is the diameter of the circle. If the unit length of the coordinate system is 54 cm, determine the inner height of the tunnel.

**Q9: **

A city is divided into regions bounded by circles centered at its city hall building. The first region is within 19 miles of city hall. The next boundary is 19 miles beyond, and so on. Determine the equation of the third circle.

- A
- B
- C
- D
- E

**Q10: **

The blueprint of a city is in a Cartesian coordinate system, where each unit represents 5 meters. Given that the circle represents one of the cityβs squares, determine the area of the square to nearest square meter. Consider .

**Q12: **

Determine, to the nearest hundredth, the area of a regular 10-sided polygon, given that the circle passes through its vertices.

**Q13: **

Given that a circle passes through the vertices of a regular pentagon and each unit of the coordinate plane represents 5 cm, find the surface area of the regular pentagon to the nearest square centimeters.

**Q14: **

Suppose that is the equation of a circle, what can you conclude about ?

- A
- B
- C
- D is any real number
- E

**Q15: **

For what values of is the equation of a circle?

- A
- B
- C
- Dany real number
- E

**Q16: **

There is a merry-go-round of radius 1.5 metres in a playground, located 10 metres north and 5 metres east from the playgroundβs entrance. Taking the playgroundβs entrance as the origin, determine the equation of the circle that represents the edge of the merry-go-round.

- A
- B
- C
- D

**Q17: **

Let us consider a circle of radius 2.

Write the equation of the circle given that its centre is located at the point (1, 3).

- A
- B
- C
- D
- E

The circle is translated five units to the left and two units up. Write its equation.

- A
- B
- C
- D
- E

**Q18: **

Let us consider a circle of radius 1.

Write the equation of the circle given that its centre is located at the origin of the coordinate plane.

- A
- B
- C
- D

The circle is translated three units to the right and two units down. Write its equation.

- A
- B
- C
- D
- E