Worksheet: Angles of Tangency

In this worksheet, we will practice using the properties of tangents to find the measure of an angle of tangency or an inscribed angle subtended by the same arc.

Q1:

𝐵 𝐶 is tangent to the circle of center 𝑀 at 𝐵. Find 𝑚𝐴𝐵𝐶.

Q2:

Given that 𝐵𝐶 is a tangent to the circle, find 𝑚𝐴𝐵𝐶.

Q3:

Given that 𝐵𝐶 is a tangent to the circle below, find 𝑚𝐴𝐵𝐶 and 𝑦.

  • A 2 2 6 , 226
  • B 1 1 3 , 113
  • C 1 1 3 , 226
  • D 2 2 6 , 113

Q4:

Given that 𝐴𝐷 is a tangent to the circle, find 𝑚𝐵𝐴𝐷.

Q5:

Given that 𝑚𝑀𝐵𝐶=28, find 𝑚𝐴.

Q6:

Given that 𝐴𝐷 is a tangent to the circle and 𝑚𝐶𝐴𝐷=97, find 𝑚𝐴𝐵𝐶 and 𝑦.

  • A 𝑚 𝐴 𝐵 𝐶 = 8 3 , 𝑦 = 8 3
  • B 𝑚 𝐴 𝐵 𝐶 = 1 6 6 , 𝑦 = 8 3
  • C 𝑚 𝐴 𝐵 𝐶 = 1 6 6 , 𝑦 = 1 6 6
  • D 𝑚 𝐴 𝐵 𝐶 = 8 3 , 𝑦 = 1 6 6

Q7:

Find 𝑚𝐴𝐶𝐷.

Q8:

Given that 𝐵𝐶 is a tangent to the circle, and 𝑚𝐷𝐴𝐵=51, determine 𝑚𝐴𝐵𝐶 and 𝑚𝐴𝐸𝐵.

  • A 3 9 , 7 8
  • B 7 8 , 3 9
  • C 5 1 , 5 1
  • D 3 9 , 3 9
  • E 7 8 , 7 8

Q9:

If 𝑚𝐴𝐵𝐶=83 and 𝑚𝑋𝐴𝐵=38, find 𝑚𝐶𝐷𝐵.

Q10:

Given that 𝐵𝐶 is a tangent to the circle, and 𝑚𝐵𝐴𝐷=63, find 𝑚𝐴𝐵𝐶 and 𝑚𝐴𝐸𝐵.

  • A 𝑚 𝐴 𝐵 𝐶 = 5 4 , 𝑚 𝐴 𝐸 𝐵 = 2 7
  • B 𝑚 𝐴 𝐵 𝐶 = 2 7 , 𝑚 𝐴 𝐸 𝐵 = 2 7
  • C 𝑚 𝐴 𝐵 𝐶 = 2 7 , 𝑚 𝐴 𝐸 𝐵 = 5 4
  • D 𝑚 𝐴 𝐵 𝐶 = 5 4 , 𝑚 𝐴 𝐸 𝐵 = 5 4

Q11:

Given that 𝑚𝐸𝐶𝐷=54 and 𝑚𝐹𝐵𝐷=78, find 𝑥 and 𝑦.

  • A54, 84
  • B48, 84
  • C78, 84
  • D78, 102
  • E54, 126

Q12:

Given that 𝑚𝐵𝐸𝐶=31, find 𝑚𝐶 and 𝑚𝐵𝐷𝐴.

  • A 𝑚 𝐶 = 2 8 , 𝑚 𝐵 𝐷 𝐴 = 6 2
  • B 𝑚 𝐶 = 2 8 , 𝑚 𝐵 𝐷 𝐴 = 5 9
  • C 𝑚 𝐶 = 2 8 , 𝑚 𝐵 𝐷 𝐴 = 2 8
  • D 𝑚 𝐶 = 2 8 , 𝑚 𝐵 𝐷 𝐴 = 1 1 8
  • E 𝑚 𝐶 = 5 9 , 𝑚 𝐵 𝐷 𝐴 = 5 9

Q13:

Given that 𝑚𝐴𝐶𝐵=80, find 𝑚𝐴𝐷𝑀.

  • A 5 0
  • B 4 0
  • C 1 0 0
  • D 8 0

Q14:

In the figure, 𝐴𝐵 is a diameter of circle 𝑀. Given that 𝑚𝐶𝐵𝐷=43, find 𝑚𝐴𝑀𝐷.

Q15:

Find 𝑚𝐵𝐴𝐶.

Q16:

Find 𝑚𝐶𝐴𝐵.

Q17:

If 𝑚𝑀𝐴𝐵=47, find 𝑚𝐴𝐶𝐷.

Q18:

If 𝐴𝐷 and 𝐴𝐸 are tangents to a circle with center 𝑀 and 𝑚𝐴=62, find 𝑚𝐸𝑀𝐷.

Q19:

Find 𝑚𝐵𝑀𝐶.

Q20:

Given the figure below, find 𝑚𝑀𝐶𝐵 and 𝑚𝐶𝐵𝐴.

  • A 6 8 , 1 1 2
  • B 3 4 , 5 6
  • C 5 6 , 3 4
  • D 3 4 , 3 4

Q21:

Given that 𝑚𝐴=84, where 𝐴𝐵 and 𝐴𝐶 are tangent to the circle at 𝐵 and 𝐶, find 𝑚𝐸.

Q22:

Given that 𝑚𝑀𝐴𝐶=36, determine 𝑚𝐵𝐴𝑀 and 𝑚𝐴𝑀𝐶.

  • A 3 6 , 5 4
  • B 5 4 , 5 4
  • C 5 4 , 3 6
  • D 3 6 , 3 6

Q23:

Given that 𝑚𝐵𝐴𝑀=35, find 𝑚𝐵𝑀𝐶.

Q24:

A circle with center 𝑀 has diameter 𝐴𝐵. If 𝐴𝐶 and 𝐵𝐷 are two tangents to the circle, what can you say about them?

  • AThey are perpendicular.
  • BThey are parallel.
  • CThey are intersecting.

Q25:

Triangle 𝐴𝐵𝐶 is right angled at 𝐵. Given that 𝑚𝐴=30, 𝐴𝐵=37.6cm, and 𝑀 is the circle that lies on 𝐴 and 𝐵 and is tangent to 𝐴𝐶 at 𝐴, determine the area of 𝐴𝐵𝑀 to the nearest tenth of a square centimeter.

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