In this worksheet, we will practice finding the power and position of a point with respect to a circle.

**Q2: **

A circle with centre and a point satisfy and . Using as an approximation for , find the area and the circumference of the circle to the nearest integer.

- Aarea , circumference
- Barea , circumference
- Carea , circumference
- Darea , circumference

**Q3: **

A circle has centre and radius . Find the power of the point with respect to the circle given that .

**Q4: **

A circle with centre has a diameter equal to 38 cm. A point satisfies . Find the power of with respect to the circle, giving your answer to the nearest integer.

- A312
- B
- C 1 395
- D

**Q5: **

A circle with centre has a radius of 8 cm. The power of a point with respect to the circle is 36. Decide whether is outside, inside, or on the circle and then find the distance between and .

- Aon the circle, 28 cm.
- Binside the circle, 44 cm.
- Coutside the circle, 10 cm.

**Q6: **

The power of the points , , and with respect to the circle are , , and . The circle has centre and a radius of 10 cm. Calculate the distance between and each of the points.

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

**Q7: **

Determine the position of a point with respect to the circle if .

- Ainside the circle
- Bon the circumference of the circle
- Coutside the circle

**Q8: **

The power of a point with respect to a circle is when its distance from the centre of that circle is 84. What is the circle’s diameter to the nearest hundredth?

**Q9: **

Given that the point is outside the circle , and is a tangent to the circle at such that , find the power of the point with respect to the circle . Round your answer to the nearest hundredth.

**Q10: **

A circle with centre has a radius of 11 cm. Point lies 5 cm from and belongs to the chord . Given that , calculate , giving your answer to the nearest hundredth.

**Q11: **

Two circles and intersect at points and , and the point satisfies and . and are the points where intersects the circle and is a tangent to . Given that and , find .

**Q12: **

Which of the following points lies on the circle of centre and radius 106?

- A
- B
- C
- D

**Q13: **

How many circles of radius 5.2 cm are there on points , with ?

**Q14: **

How many points lie outside the circle?

- A1
- B2
- C3
- D7

**Q15: **

Circle has diameter 6 cm. If , what is the position of point with respect to the circle?

- Aon
- Binside
- Cat the centre of
- Doutside

**Q16: **

Which points lie on the circle?

- A
- B
- C
- D

**Q17: **

Which points lie outside the circle?

- A
- B
- C
- D

**Q18: **

Circle has radius 3 cm. If , what is the position of point with respect to the circle?

- Aon
- Boutside
- Cinside

**Q19: **

How many circles can pass through two points?

- A2
- B1
- C0
- Dinfinite

**Q20: **

Which points lie outside the circle?

- A
- B
- C
- D

**Q21: **

How many circles can pass through three collinear points?

- A2
- B1
- Cinfinite
- D0

**Q22: **

How many circles pass through a given point?

- A2
- B1
- C0
- Dinfinitely many

**Q23: **

Which points lie on the circle?

- A
- B
- C
- D

**Q24: **

Which points lie inside the circle?

- A
- B
- C
- D

**Q25: **

Which points lie on the circle?

- A
- B
- C
- D