In this worksheet, we will practice identifying circumscribed polygons and solving problems involving them.

**Q1: **

Is the following statement true or false? In a circle, all of the inscribed angles which intercept the same arc are equal.

- Atrue
- Bfalse

**Q3: **

Find the perimeter of the .

**Q4: **

Find the lengths of and .

- A 31.66 cm, 41.49 cm
- B 36.58 cm, 45.41 cm
- C 41.49 cm, 49.32 cm
- D 31.66 cm, 49.32 cm

**Q5: **

In the following figure, find the perimeter of the square given that the length of the circle’s radius .

**Q6: **

Which of the following diagrams shows a circumscribed polygon?

- AC
- BA
- CD
- DB

**Q7: **

A regular pentagon is circumscribed around a circle of radius 2 cm. Find the length of one side of the pentagon. Give your answer correct to one decimal place.

**Q8: **

In the figure, , , and . Find the perimeter and the area of .

- A
412 cm, 7 857 cm
^{2} - B
206 cm, 10 300 cm
^{2} - C
206 cm, 7 857 cm
^{2} - D
412 cm, 10 300 cm
^{2}

**Q9: **

Given that is an equilateral triangle whose sides touch circle and that the coordinates of point are , determine the equation of circle .

- A
- B
- C
- D

**Q10: **

The circle centre is inscribed in the equilateral triangle of side 63. What is the circumference of the circle?

- A
- B
- C
- D
- E

**Q11: **

In a triangle , , , and . A circle with centre is drawn so that is a radius and is bisected at . Find the length of the diameter.