Lesson: Power of a Point

In this lesson, we will learn how to find the power and position of a point with respect to a circle.

Sample Question Videos

  • 02:11

Worksheet: Power of a Point • 25 Questions • 1 Video

Q1:

A point is at a distance 40 from the centre 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 centre and a point satisfy and . Using as an approximation for , find the area and the circumference of the circle to the nearest integer.

Q3:

A circle has centre 𝑀 and radius π‘Ÿ = 2 1 . Find the power of the point 𝐴 with respect to the circle given that 𝐴 𝑀 = 2 5 .

Q4:

A circle with centre 𝑁 has a diameter equal to 38 cm. A point 𝐡 satisfies 𝑁 𝐡 = 7 c m . Find the power of 𝐡 with respect to the circle, giving your answer to the nearest integer.

Q5:

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

Q6:

The power of the points 𝐴 , 𝐡 , and 𝐢 with respect to the circle 𝐾 are 𝑃 ( 𝐴 ) = 4 𝐾 , 𝑃 ( 𝐡 ) = 1 4 𝐾 , and 𝑃 ( 𝐢 ) = βˆ’ 1 𝐾 . The circle 𝐾 has centre 𝑀 and a radius of 10 cm. Calculate the distance between 𝑀 and each of the points.

Q7:

Determine the position of a point 𝐴 with respect to the circle 𝑁 if 𝑃 ( 𝐴 ) = 8 1 4 𝑁 .

Q8:

The power of a point with respect to a circle is βˆ’ 5 7 5 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 𝐴 is outside the circle 𝑀 , and 𝐴 𝐷 is a tangent to the circle at 𝐷 such that 𝐴 𝐷 = 1 7 . 6 5 c m , find the power of the point 𝐴 with respect to the circle 𝑀 . Round your answer to the nearest hundredth.

Q10:

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

Q11:

Two circles 𝑀 and 𝑁 intersect at points 𝐴 and 𝐡 , and the point 𝐢 satisfies 𝐢 ∈  𝐡 𝐴 and 𝐢 βˆ‰ 𝐡 𝐴 . 𝐷 and 𝐸 are the points where 𝐢 𝐸 intersects the circle 𝑀 and οƒͺ 𝐢 𝐹 is a tangent to 𝑁 . Given that 𝐢 𝐷 = 7 and 𝐷 𝐸 = 1 2 , find 𝑃 ( 𝐢 )  .

Q12:

Which of the following points lies on the circle of centre ( 0 , 0 ) and radius 106?

Q13:

How many circles of radius 5.2 cm are there on points 𝐴 , 𝐡 with 𝐴 𝐡 = 2 4 c m ?

Q14:

How many points lie outside the circle?

Q15:

Circle 𝑀 has diameter 6 cm. If 𝑀 𝐴 = 1 0 c m , what is the position of point 𝐴 with respect to the circle?

Q16:

Which points lie on the circle?

Q17:

Which points lie outside the circle?

Q18:

Circle 𝑀 has radius 3 cm. If 𝑀 𝐴 = 1 c m , what is the position of point 𝐴 with respect to the circle?

Q19:

How many circles can pass through two points?

Q20:

Which points lie outside the circle?

Q21:

How many circles can pass through three collinear points?

Q22:

How many circles pass through a given point?

Q23:

Which points lie on the circle?

Q24:

Which points lie inside the circle?

Q25:

Which points lie on the circle?

Preview

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.