Worksheet: Applications of Angles in Semicircles

In this worksheet, we will practice applying the fact that the angle inscribed in a semicircle is a right angle, in a variety of questions.

Q1:

Find .

Q2:

Given that , find and .

• A ,
• B ,
• C ,
• D ,

Q3:

Find and .

• A ,
• B ,
• C ,
• D ,

Q4:

Given that , find .

• A
• B
• C
• D

Q5:

Given that , find the length of .

Q6:

Given that and , find and .

• A ,
• B ,
• C ,
• D ,

Q7:

Find .

Q8:

Given that is a rectangle, in which , , and , find the length of .

Q9:

Given that , find .

Q10:

Point is outside a circle centre , and meets the circle in and . Suppose that is tangent to the circle at and . What is ?

Q11:

In the given figure, is a diameter.

What is the size of angle ?

• A
• B
• C
• D
• E

Given that the size of angle , find the size of angle .

• A
• B
• C
• D
• E

Calculate the size of angle .

• A
• B
• C
• D
• E

Q12:

Find .

Q13:

Given that , find .

• A
• B
• C
• D

Q14:

Given that , find .

• A
• B
• C
• D

Q15:

Given that and , find and .

• A ,
• B ,
• C ,
• D ,