Worksheet: Circumscribed Polygons

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, 𝐴𝑍=7.5cm, 𝐡𝑍=14.5cm, and 𝐴𝐢=20cm. Given that all sides of triangle 𝐴𝐡𝐢 are tangent to the shown circle, determine the length of 𝐡𝐢.

Q3:

Find the perimeter of the △𝐴𝐡𝐢.

Q4:

Find the lengths of 𝐷𝐡 and 𝐸𝐢.

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

Q5:

In the following figure, find the perimeter of the square 𝐿𝑀𝑁𝑂 given that the length of the circle’s radius =3cm.

Q6:

Which of the following diagrams shows a circumscribed polygon?

  • AC
  • BB
  • CD
  • DA

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‘Ÿ=50cm, 𝐴𝐡=97cm, and 𝐢𝐷=109cm. Find the perimeter and the area of 𝐴𝐡𝐢𝐷.

  • A 206 cm, 7,857 cm2
  • B 412 cm, 7,857 cm2
  • C 206 cm, 10,300 cm2
  • D 412 cm, 10,300 cm2

Q9:

Given that 𝐴𝐡𝐢 is an equilateral triangle whose sides touch circle 𝑀 and that the coordinates of point 𝐡 are (βˆ’7,0), determine the equation of circle 𝑀.

  • A ο€Ό π‘₯ + 7 2  + ο€Ώ 𝑦 + 7 √ 3 6  = 4 9 1 2  
  • B ο€Ό π‘₯ βˆ’ 7 2  + ο€Ώ 𝑦 βˆ’ 7 √ 3 6  = 4 9 1 2  
  • C ο€Ό π‘₯ + 7 2  + ο€Ώ 𝑦 + 7 √ 3 2  = 4 9 4  
  • D ο€Ό π‘₯ + 7 2  + ο€Ώ 𝑦 + 7 √ 3 3  = 4 9 3  

Q10:

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

  • A 4 2 √ 3
  • B 2 1 √ 3
  • C 2 1 πœ‹ √ 3
  • D 2 1 πœ‹
  • E 4 2 πœ‹ √ 3

Q11:

In a triangle π‘‹π‘Œπ‘, π‘‹π‘Œ=5cm, 𝑋𝑍=3cm, and π‘Œπ‘=4cm. A circle with center 𝑀 is drawn so that 𝑀𝑍 is a radius and π‘‹π‘Œ is bisected at 𝑀. Find the length of the diameter.

Q12:

In the shown figure, 𝐴𝑍=7.5cm, 𝐡𝑍=13.5cm, and 𝐴𝐢=19cm. Given that all sides of triangle 𝐴𝐡𝐢 are tangent to the shown circle, determine the length of 𝐡𝐢.

Q13:

Circle 𝑀 is inscribed in △𝐴𝐡𝐢. Determine the triangle’s area.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.