# Worksheet: The Power of a Point Theorem

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

**Q3: **

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

**Q4: **

A circle with center 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.

- A
- B312
- C1,395
- D

**Q5: **

A circle with center 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 center 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 .

- Aoutside the circle
- Binside the circle
- Con the circumference of the circle

**Q8: **

The power of a point with respect to a circle is when its distance from the center of that circle is 84. What is the circleβs 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 center 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: **

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

**Q13: **

A line intersects a circle with center . Point lies on and is inside the circle. If the radius of the circle is 8 cm, , and we set , in what interval does the value of belong?

- A
- B
- C
- D

**Q14: **

A circle has a radius of 90 cm. A point lies on the circle at a distance of cm from the center. Which of the following is true?

- A
- B
- C