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

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 π and radius π = 2 1 . Find the power of the point π΄ with respect to the circle given that π΄ π = 2 5 .

Q4:

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

Q5:

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

Q6:

The power of the points π΄ , π΅ , and πΆ with respect to the circle πΎ are π ( π΄ ) = 4 πΎ , π ( π΅ ) = 1 4 πΎ , and π ( πΆ ) = β 1 πΎ . The circle πΎ has centre π and a radius of 10 cm. Calculate the distance between π and each of the points.

Q7:

Determine the position of a point π΄ with respect to the circle π if π ( π΄ ) = 8 1 4 π .

Q8:

The power of a point with respect to a circle is β 5 7 5 when its distance from the centre of that circle is 84. What is the circleβs diameter to the nearest hundredth?

Q9:

Given that the point π΄ is outside the circle π , and π΄ π· is a tangent to the circle at π· such that π΄ π· = 1 7 . 6 5 c m , find the power of the point π΄ with respect to the circle π . Round your answer to the nearest hundredth.

Q10:

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

Q11:

Two circles π and π intersect at points π΄ and π΅ , and the point πΆ satisfies πΆ β ο« π΅ π΄ and πΆ β π΅ π΄ . π· and πΈ are the points where πΆ πΈ intersects the circle π and οͺ πΆ πΉ is a tangent to π . Given that πΆ π· = 7 and π· πΈ = 1 2 , find π ( πΆ ) ο .

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 π΄ , π΅ with π΄ π΅ = 2 4 c m ?

Q14:

How many points lie outside the circle?

Q15:

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

Q16:

Which points lie on the circle?

Q17:

Which points lie outside the circle?

Q18:

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

Q19:

How many circles can pass through two points?

Q20:

Q21:

How many circles can pass through three collinear points?

Q22:

How many circles pass through a given point?

Q23:

Q24:

Which points lie inside the circle?

Q25:

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