# Worksheet: Positions of Points, Straight Lines, and Circles with respect to Circles

In this worksheet, we will practice finding the positions of points, straight lines, and circles with respect to other circles.

**Q2: **

In the given figure, is tangent to the circle with centre .

If the length of is 3, the length of is 5, and the length of is 40, what are the lengths of and ?

- A 20, 20
- B 10, 30
- C 30, 10
- D 15, 25

**Q3: **

The radii of the two circles on the common centre are 3 cm and 4 cm. What is the length of ?

**Q4: **

Given that , find .

**Q5: **

Given that is a tangent to the circle with centre and , find .

**Q6: **

Identify all the radii of circle .

- A
- B
- C

**Q7: **

If is a tangent to the circle at the point , and , what is ?

**Q8: **

Given that is a tangent to the circle at the point , , and the point is the midpoint of , find the value of .

**Q9: **

Given that is a tangent to the circle and , calculate .

**Q10: **

The circumference of circle is 259 and is tangent at . Calculate the length of to the nearest hundredth.

**Q11: **

Given that , find and .

- A ,
- B ,
- C ,
- D ,

**Q12: **

In the figure, two circles with centres and touch externally at which is a point on the common tangent , where is a common tangent. Suppose and . Find to the nearest tenth.

**Q13: **

Describe the position of the straight line with respect to the circle .

- AThe straight line is a tangent to the circle.
- BThe straight line is outside the circle.
- CThe straight line is a secant to the circle.

**Q14: **

Where is the point in relation to the circle ?

- Aoutside
- Binside
- Con

**Q15: **

On which of the following does the point lie?

- Athe-axis
- Bthe-axis
- Cthe circle
- Dthe straight line