Worksheet: Relations between Circles

In this worksheet, we will practice using the relation between two circles touching internally or externally and the properties that result from this relation to solve problems.

Q1:

Two circles 𝑀 and 𝑁 intersect at points 𝐴 and 𝐵 , where 𝐵 𝐴 = 1 5 c m . The point 𝐶 satisfies 𝐶 𝐵 𝐴 and 𝐶 𝐵 𝐴 . 𝐹 is a point on the circle 𝑁 such that 𝐶 𝐹 is a tangent of 𝑁 . Also, 𝐶 𝐸 intersects the circle 𝑀 at 𝐷 and 𝐸 , where 𝐶 𝐷 = 8 c m and 𝐷 𝐸 = 5 c m . Find the length of 𝐶 𝐴 and 𝐶 𝐹 to two decimal places.

  • A 𝐶 𝐴 = 5 . 1 6 c m , 𝐶 𝐹 = 1 0 . 2 0 c m
  • B 𝐶 𝐴 = 2 0 . 1 6 c m , 𝐶 𝐹 = 1 0 . 2 0 c m
  • C 𝐶 𝐴 = 2 . 3 1 c m , 𝐶 𝐹 = 5 2 . 0 0 c m
  • D 𝐶 𝐴 = 4 4 . 6 4 c m , 𝐶 𝐹 = 5 2 . 0 0 c m

Q2:

Given that 𝐵 𝐶 = 4 1 . 7 c m and 𝑀 𝐷 = 6 0 c m , find the length of 𝐴 𝐷 to the nearest tenth.

Q3:

Find 𝑚 𝐵 𝐴 𝐷 .

Q4:

In the figure, circles 𝑀 and 𝑁 intersect at 𝐴 and 𝐵 , and 𝑚 𝐸 = 4 8 . 3 . What is 𝑚 𝑍 𝑁 𝑋 ?

Q5:

Two congruent circles of radius 𝑟 cm intersect. Their centres are 56 cm apart, and their common chord has a length of 42 cm. Determine 𝑟 .

Q6:

Suppose 𝐴 𝑀 = 4 9 c m . What is 𝐴 𝐵 ?

Q7:

In the figure, circles 𝑀 and 𝑁 intersect at 𝐴 and 𝐵 . If 𝐺 𝐶 = 𝐶 𝐸 and 𝑚 𝐶 𝑀 𝑁 = ( 6 𝑥 6 ) , determine 𝑥 to the nearest tenth.

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