# Worksheet: Angles Formed by Lines Intersecting outside a Circle

Q1:

In the given figure, find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q2:

Given that is tangent to the circle and that and lie on the circle, determine the value of to the nearest tenth.

Q3:

is the regular pentagon drawn inside the circle , is a tangent to the circle at , and is a tangent to the circle at . Find .

Q4:

Given that and are two tangents to the circle , and , determine .

• A
• B
• C
• D

Q5:

Find .

• A
• B
• C
• D

Q6:

Find .

Q7:

Given that is the measure of the major arc , find the value of .

Q8:

Find the value of .

Q9:

Find .

Q10:

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

• A
• B
• C
• D

Q11:

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

Q12:

Circle has radius 65. Suppose is on a line and is perpendicular to . If what can be said of how lies with respect to the circle?

• A is outside of circle
• B is a tangent to circle
• C is a secant to circle

Q13:

Given , and , find the length of rounded to the nearest hundredth.

Q14:

Given that and , find .

Q15:

Given that , find .

• A
• B
• C
• D

Q16:

If , find .

• A
• B
• C
• D

Q17:

Find .

Q18:

Find length to the nearest integer.

Q19:

Lines and are tangent to circle . If , what is ?

• A
• B
• C
• D

Q20:

In the figure, find the value of .

• A
• B
• C
• D

Q21:

Given that is a diameter in the circle , is a tangent to the circle at , and , find .

• A
• B
• C
• D

Q22:

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

• A
• B
• C
• D

Q23:

In the figure, and are tangents to . What is ?

• A
• B
• C
• D