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In this lesson, we will learn how to find the positions of points, straight lines, and circles with respect to other circles.

Q1:

In the figure below, ο« π΄ π΅ is a tangent to the circle π at π΅ , πΆ π· is a diameter, π β π΅ π΄ π = π₯ , and π β π π· π΅ = 2 π₯ β 5 5 . Find the value of π₯ in degrees.

Q2:

In the figure below, ο« π΄ π΅ is a tangent to the circle π at π΅ , πΆ π· is a diameter, π β π΅ π΄ π = π₯ , and π β π π· π΅ = 2 π₯ β 5 . Find the value of π₯ in degrees.

Q3:

Given that π β π π πΏ = 1 2 2 β , find π β π .

Q4:

In the given figure, β ο© ο© ο© ο© β π π is tangent to the circle with centre π΅ .

If the length of π΄ π is 3, the length of π΅ π is 5, and the length of π΄ π΅ is 40, what are the lengths of π΄ π and π π΅ ?

Q5:

Given that β ο© ο© ο© ο© β π΅ πΆ is a tangent to the circle with centre π and β π΄ π π· = 9 7 β , find β πΆ π΅ π· .

Q6:

Identify all the radii of circle .

Q7:

If β ο© ο© ο© ο© β πΈ π· is a tangent to the circle at the point π΅ , and π β πΈ π΅ πΆ = 4 0 β , what is π β π΄ πΆ π΅ ?

Q8:

Given that π΄ π΅ is a tangent to the circle π at the point π΅ , π β π΅ π πΆ = 3 π β π΄ , and the point πΆ is the midpoint of π· πΈ , find the value of π₯ .

Q9:

Given that ο« π΄ π· is a tangent to the circle and π β π· π΄ πΆ = 9 0 β , calculate π β π΄ πΆ π΅ .

Q10:

Given that π β πΆ π· πΈ = 8 9 β , find π β π· π΅ πΆ and π β π΄ π· π΅ .

Q11:

The circumference of circle π is 259 and ο« π π is tangent at π . Calculate the length of π π to the nearest hundredth.

Q12:

In the figure, two circles with centres π and π touch externally at π΄ which is a point on the common tangent β β πΏ , where π΄ π΅ is a common tangent. Suppose π΄ π΅ = π π = 4 5 . 5 c m and π΅ πΆ = 3 0 . 5 c m . Find π΄ π to the nearest tenth.

Q13:

The radii of the two circles on the common centre π are 3 cm and 4 cm. What is the length of π΄ π΅ ?

Q14:

On which of the following does the point lie?

Q15:

Describe the position of the straight line πΏ βΆ 5 π₯ + 4 π¦ β 1 = 0 with respect to the circle π₯ + π¦ + 6 π₯ β 8 π¦ + 9 = 0 2 2 .

Q16:

Where is the point ( 4 , 2 ) in relation to the circle ( π₯ β 4 ) + ( π¦ β 1 ) = 1 2 2 ?

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