# Worksheet: The Power of a Point Theorem

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

Q1:

A point is at a distance 40 from the center of a circle. If its power with respect to the circle is 81, what is the radius of the circle, rounded to the nearest integer?

Q2:

A circle with center and a point satisfy and . Using , 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 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 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 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