# 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:

is tangent to the circle of center at . Find . Q2:

Given that is a tangent to the circle, find . Q3:

Given that is a tangent to the circle below, find and . • A, 226
• B, 113
• C, 226
• D, 113

Q4:

Given that is a tangent to the circle, find . Q5:

Given that , find . Q6:

Given that is a tangent to the circle and , find and . • A,
• B,
• C,
• D,

Q7:

Find . Q8:

Given that is a tangent to the circle, and , determine and . • A,
• B,
• C,
• D,
• E,

Q9:

If and , find . Q10:

Given that is a tangent to the circle, and , find and . • A,
• B,
• C,
• D,

Q11:

Given that and , find and . • A54, 84
• B48, 84
• C78, 84
• D78, 102
• E54, 126

Q12:

Given that , find and . • A,
• B,
• C,
• D,
• E,

Q13:

Given that , find . Q14:

In the figure, is a diameter of circle . Given that , find . Q15:

Find . Q16:

Find . Q17:

If , find . Q18:

If and are tangents to a circle with center and , find . Q19:

Find . Q20:

Given the figure below, find and . • A,
• B,
• C,
• D,

Q21:

Given that , where and are tangent to the circle at and , find . Q22:

Given that , determine and . • A,
• B,
• C,
• D,

Q23:

Given that , find . Q24:

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

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

Q25:

Triangle is right angled at . Given that , , and is the circle that lies on and and is tangent to at , determine the area of to the nearest tenth of a square centimeter.