Worksheet: Circle Theorems

In this worksheet, we will practice recognizing and applying circle theorems to find unknown angle measures in circles.

Q1:

In the following figure, 𝐵𝐶 is a tangent to circle with center 𝑀 at point 𝐵. Find the length of 𝐶𝐸 to the nearest tenth.

Q2:

In the the following figure, 𝐸𝐹 and 𝐸𝐺 are tangents to the circle at points 𝐵 and 𝐶, respectively, 𝑚𝐴𝐵𝐹=40, and 𝑚𝐴𝐶𝐷=65. Find 𝑚𝐵𝐸𝐶.

Q3:

In the following figure, 𝐷𝐹 is a tangent to circle of center 𝑀 at point 𝐵. Find 𝑚𝐴𝐷𝐵.

Q4:

In the following figure, 𝐸𝐹 is a tangent to circle 𝑀 at point 𝐵 and 𝑚𝐴𝐵𝐸=35. Find 𝑚𝐶𝐵𝐹.

Q5:

In the following figure, 𝐸𝐹 is a tangent to circle of center 𝑀 at point 𝐶, 𝐴𝑁=𝐵𝑁, and 𝑚𝐴𝐶𝐸=70. Find 𝑚𝐵𝑀𝐷.

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