Worksheet: Intersection of Chords and Tangents in a Circle

In this worksheet, we will practice finding the measures of the resulting angles from the intersection of chords and tangents in a circle.

Q1:

Find the value of 𝑧 .

Q2:

In the given figure, 𝑚 𝐶 𝐸 𝑚 𝐵 𝐷 = 1 0 4 . Determine 𝑚 𝐴 .

Q3:

Determine 𝑚 𝐶 𝐵 .

Q4:

In the given figure, find 𝑚 𝐴 𝐶 + 𝑚 𝐵 𝐷 .

Q5:

Find the value of 𝑥 .

Q6:

Given that 𝑚 𝐴 = 3 1 , find 𝑥 .

Q7:

Find 𝑥 .

  • A 7 7
  • B 6 0
  • C 3 0
  • D 1 0 3
  • E 2 0 6

Q8:

Find 𝑥 .

Q9:

Find 𝑚 𝐵 𝐴 𝐶 .

  • A 2 3 9
  • B 1 2 1
  • C 5 9
  • D 6 2
  • E 2 4 2

Q10:

Given that, in the shown figure, 𝑦 = ( 𝑥 2 ) and 𝑧 = ( 2 𝑥 + 2 ) , determine the value of 𝑥 .

Q11:

Given that 𝑚 𝐶 𝐴 𝐵 = 7 6 , find the value of 𝑥 .

Q12:

Given that 𝐵 𝐶 is a tangent to the circle, find 𝑚 𝐴 𝐵 𝐶 .

Q13:

Find 𝑥 .

Q14:

The circle in the given figure has an arc with a size of .

What is the size of the central angle?

  • A
  • B
  • C
  • D
  • E

What is the size of the inscribed angle?

  • A
  • B
  • C
  • D
  • E

What is the size of the circumscribed angle?

  • A
  • B
  • C
  • D
  • E

Q15:

Find 𝑥 .

Q16:

Find the value of 𝑥 .

Q17:

Given that, in the shown figure, 𝑦 = ( 𝑥 4 ) and 𝑧 = ( 2 𝑥 + 2 ) , determine the value of 𝑥 .

Q18:

In the given figure, find 𝑚 𝐴 𝐶 + 𝑚 𝐵 𝐷 .

Q19:

Find 𝑥 .

  • A 1 0 4
  • B 3 6
  • C 1 8
  • D 7 6
  • E 1 5 2

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