Worksheet: Applications of Intersecting Chords and Secants

In this worksheet, we will practice finding the length of a part of a chord or a secant that intersects with another chord or secant, inside or outside a circle.

Q1:

If , , , find the length of .

Q2:

If , , and , find the lengths of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q3:

In the figure shown, the circle has a radius of 12 cm, , and . Determine the distance from to the centre of the circle, , and the length of , rounding your answers to the nearest tenth.

• A 19.6 cm, 20.2 cm
• B 11.5 cm, 20.2 cm
• C 3.4 cm, 26.6 cm
• D 3.4 cm, 20.5 cm

Q4:

Given that , , , and , find the value of .

• A
• B
• C
• D

Q5:

Are the points , , , and lying on a circle?

• Ayes
• Bno

Q6:

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

Q7:

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

Q8:

A circle has centre 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 ,