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In this lesson, we will learn how to identify circumscribed polygons and how to solve 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.

Q2:

In the shown figure, π΄ π = 7 . 5 c m , π΅ π = 1 4 . 5 c m , and π΄ πΆ = 2 0 c m . Given that all sides of triangle π΄ π΅ πΆ are tangent to the shown circle, determine the length of π΅ πΆ .

Q3:

Find the perimeter of the β³ π΄ π΅ πΆ .

Q4:

Find the lengths of π· π΅ and πΈ πΆ .

Q5:

In the following figure, find the perimeter of the square given that the length of the circleβs 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, π = 5 0 c m , π΄ π΅ = 9 7 c m , and πΆ π· = 1 0 9 c m . Find the perimeter and the area of π΄ π΅ πΆ π· .

Q9:

Given that π΄ π΅ πΆ is an equilateral triangle whose sides touch circle π and that the coordinates of point π΅ are ( β 7 , 0 ) , determine the equation of circle π .

Q10:

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

Q11:

In a triangle π π π , π π = 5 c m , π π = 3 c m , and π π = 4 c m . A circle with centre π is drawn so that π π is a radius and π π is bisected at π . Find the length of the diameter.

Q12:

In the shown figure, π΄ π = 7 . 5 c m , π΅ π = 1 3 . 5 c m , and π΄ πΆ = 1 9 c m . Given that all sides of triangle π΄ π΅ πΆ are tangent to the shown circle, determine the length of π΅ πΆ .

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