Worksheet: Circumscribed Polygons

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In this worksheet, we will practice identifying circumscribed polygons and using their properties to find areas or missing lengths.

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

Q2:

In the shown figure, , , and . Given that all sides of triangle are tangent to the shown circle, determine the length of .

Q3:

Find the perimeter of the .

Q4:

Find the lengths of and .

A36.58 cm, 45.41 cm
B31.66 cm, 49.32 cm
C41.49 cm, 49.32 cm
D31.66 cm, 41.49 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?

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 .

A206 cm, 7,857 cm²
B412 cm, 7,857 cm²
C206 cm, 10,300 cm²
D412 cm, 10,300 cm²

Q9:

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

Q10:

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

Q11:

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

Q12:

In the shown figure, , , and . Given that all sides of triangle are tangent to the shown circle, determine the length of .

Q13:

Circle is inscribed in . Determine the triangle’s area.