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 οƒͺ𝐡𝐢 is a tangent to the circle below, find π‘šβˆ π΄π΅πΆ.

Q2:

Find π‘šβˆ πΆπ΄π΅.

Q3:

Given that οƒͺ𝐡𝐢 is a tangent to the circle, find π‘šβˆ π΄π΅πΆ.

Q4:

Given that π‘šβˆ πΈπΆπ·=54∘ and π‘šβˆ πΉπ΅π·=78∘, find π‘₯ and 𝑦.

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

Q5:

Find π‘šβˆ πΈπΆπ·.

Q6:

Find π‘šβˆ πΈπ·πΆ.

Q7:

Find π‘šβˆ π΅π΄πΆ.

Q8:

⃖⃗𝐡𝐢 is tangent to the circle of center 𝑀 at 𝐡. Find π‘šβˆ π΄π΅πΆ.

Q9:

Suppose that βƒ–οƒ©οƒ©οƒ©οƒ©οƒ©βƒ—π‘‹π‘Œ is a tangent to the circle with center 𝑀 at 𝐡, 𝐡𝐴βˆ₯𝑀𝐢, and π‘šβˆ π΄π΅π‘Œ=51.8∘. Find π‘šβˆ πΆπ΅π‘‹.

Q10:

In the given figure, if 𝐴𝐷≠𝐴𝐡≠𝐡𝐢, which of the following is a tangent to the circle that passes through the vertices of the triangle 𝐴𝐡𝐸?

  • A𝐴𝐷
  • B𝐸𝐷
  • C𝐡𝐢
  • Dοƒͺπ΅π‘Œ
  • E𝐸𝐢

This lesson includes 30 additional questions and 279 additional question variations for subscribers.

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