# Worksheet: Power of a Point

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?

• A41
• B19
• C21
• D39

Q2:

A circle with center 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:

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.

Q4:

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

• A4
• B
• C
• D184

Q5:

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

• A
• B89
• C1
• D

Q6:

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

• A
• B936
• C26
• D

Q7:

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

• A
• B
• C
• D

Q8:

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

Q9:

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 .

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.

• A 58.79 cm
• B 21.91 cm
• C 9.80 cm
• D 26.29 cm

Q11:

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.

• A312
• B
• C 1β395
• D

Q12:

How many points lie outside the circle?

• A1
• B2
• C3
• D7

Q13:

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

Q14:

A circle with center has a radius of 6 cm. The power of a point with respect to the circle is . Decide whether is outside, inside, or on the circle and then find the distance between and .

• Aon the circle, 41 cm
• Boutside the circle, 29 cm
• Cinside the circle, 1 cm

Q15:

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

• Aon
• Binside
• Cat the center 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:

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 , ,

Q19:

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

• Ainside the circle
• Bon the circumference of the circle
• Coutside the circle

Q20:

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

• Aon
• Boutside
• Cinside

Q21:

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 circleβs diameter to the nearest hundredth?

• A161.01
• B87.36
• C80.50
• D174.71

Q22:

The power of a point with respect to a circle is 297 when its distance from the center of that circle is 94. What is the circleβs diameter to the nearest hundredth?

• A191.13
• B92.41
• C95.57
• D184.81

Q23:

How many circles can pass through two points?

• A2
• B1
• C0
• Dinfinite

Q24:

Which points lie outside the circle?

• A
• B
• C
• D

Q25:

How many circles can pass through three collinear points?

• A2
• B1
• Cinfinite
• D0