# Lesson Worksheet: Special Segments in a Circle Mathematics • 11th Grade

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:

Given that , , and , find the length of . Q2:

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

Q3:

If , , , find the length of . Q4:

Given that the points , , , and lie on a circle, find the length of . Q5:

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,

Q6:

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

Q7:

Find length to the nearest integer. Q8:

Given that is tangent to the circle and that and lie on the circle, determine the value of to the nearest tenth. Q9:

Given that , , , and , do the points , , , and lie on a circle? • AYes
• BNo

Q10:

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