# Worksheet: Special Segments in a Circle

In this worksheet, we will practice using the theorems of intersecting chords, secants, or tangents and secants to find missing lengths in a circle.

Q1:

If , , and , find the lengths of and . • A,
• B,
• C,
• D,

Q2:

Given that , , , and , do the points , , , and lie on a circle? • Ayes
• Bno

Q3:

In the following figure, find the value of . Q4:

Given that , , and , find the length of . Q5:

Points , , and , , are collinear. Suppose that , , , and . Do points , , , and lie on a circle? • Ano
• Byes

Q6:

What is the radius of circle ? Q7:

In the following figure, find the value of . Q8:

Given that , , and , find the length of . Q9:

If , , and , find the lengths of and . • A,
• B,
• C,
• D,
• E,

Q10:

Given that , , , and , do the points , , , and lie on a circle? • Ano
• Byes

Q11:

Points , , and , , are collinear. Suppose that , , , and . Do points , , , and lie on a circle? • Ano
• Byes

Q12:

and are two chords of a circle of center and radius 26. Suppose that is perpendicular to both and and contains a point with . Find the lengths of and .

• A,
• B,
• C,
• D,

Q13:

If , , and , find the lengths of and . • A,
• B,
• C,
• D,
• E,

Q14:

A circle has center and radius 13 cm. A line passes through the points , , and where and are on the circle, is 25 cm from the point , and . Calculate the length of and the perpendicular distance between the line and the point . Round your answers to 2 decimal places.

• A,
• B,
• C,
• D,

Q15:

Given that the points , , , and lie on a circle, find the length of . Q16:

In the figure shown, the circle has a radius of 12 cm, , and . Determine the distance from to the center of the circle, , and the length of , rounding your answers to the nearest tenth. • A19.6 cm, 20.2 cm
• B3.4 cm, 26.6 cm
• C3.4 cm, 20.5 cm
• D11.5 cm, 20.2 cm

Q17:

In the figure below, is a diameter of the circle , , , , and . Find the length of . Q18:

If , , , find the length of . Q19:

Are the points , , , and lying on a circle? • Ano
• Byes

Q20:

Given that , , , and , find the value of . • A
• B
• C
• D

Q21:

Given that the circle shown below has a radius of 25 cm, , and , find the length of . • A14 cm
• B30 cm
• C cm
• D25 cm

Q22:

and are two chords of a circle intersecting at . Find , where , , and .

• A2
• B20
• C5
• D12.8
• E5.6

Q23:

and are two intersecting line segments at inside a circle, where , , , and . Are and chords?

• AYes
• BNo

Q24:

In the given figure, , , and . Find the length of . Q25:

Find the value of . 