Worksheet: The Power of a Point Theorem
In this worksheet, we will practice finding the power of a point with respect to a circle.
A circle has center and radius . Find the power of the point with respect to the circle given that .
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 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
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 , ,
Determine the position of a point with respect to the circle if .
- Aoutside the circle
- Binside the circle
- Con the circumference of the circle
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 circle’s diameter to the nearest hundredth?
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.
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.
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 .
How many circles of radius 5.2 cm are there on points , with ?
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 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?