Lesson Worksheet: Angles of Tangency Mathematics • 11th Grade

In this worksheet, we will practice identifying the angle of tangency in a circle and find its measure using the measure of its subtended arc, inscribed angle, or central angle subtended by the same arc.

Q1:

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

Q2:

Find 𝑚𝐶𝐴𝐵.

Q3:

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

Q4:

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

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

Q5:

Find 𝑚𝐸𝐶𝐷.

Q6:

Find 𝑚𝐸𝐷𝐶.

Q7:

Find 𝑚𝐵𝐴𝐶.

Q8:

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

Q9:

Suppose that 𝑋𝑌 is a tangent to the circle with center 𝑀 at 𝐵, 𝐵𝐴𝑀𝐶, and 𝑚𝐴𝐵𝑌=51.8. Find 𝑚𝐶𝐵𝑋.

Q10:

In the given figure, if 𝐴𝐷𝐴𝐵𝐵𝐶, which of the following is a tangent to the circle that passes through the vertices of the triangle 𝐴𝐵𝐸?

  • A𝐴𝐷
  • B𝐸𝐷
  • C𝐵𝐶
  • D𝐵𝑌
  • E𝐸𝐶

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