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.

**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 ,