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Worksheet: Circumscribed Polygons

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

Q1:

In the shown figure, 𝐴 𝑍 = 7 . 5 c m , 𝐡 𝑍 = 1 4 . 5 c m , and 𝐴 𝐢 = 2 0 c m . Given that all sides of triangle 𝐴 𝐡 𝐢 are tangent to the shown circle, determine the length of 𝐡 𝐢 .

Q2:

In the shown figure, 𝐴 𝑍 = 7 . 5 c m , 𝐡 𝑍 = 1 3 . 5 c m , and 𝐴 𝐢 = 1 9 c m . Given that all sides of triangle 𝐴 𝐡 𝐢 are tangent to the shown circle, determine the length of 𝐡 𝐢 .

Q3:

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

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

Q4:

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

Q5:

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.

Q6:

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

Q7:

Which of the following diagrams shows a circumscribed polygon?

  • AC
  • BA
  • CD
  • DB

Q8:

In a triangle 𝑋 π‘Œ 𝑍 , 𝑋 π‘Œ = 5 c m , 𝑋 𝑍 = 3 c m , and π‘Œ 𝑍 = 4 c m . A circle with center 𝑀 is drawn so that 𝑀 𝑍 is a radius and 𝑋 π‘Œ is bisected at 𝑀 . Find the length of the diameter.

  • A 4 cm
  • B 3 cm
  • C 12 cm
  • D 5 cm

Q9:

Find the lengths of 𝐷 𝐡 and 𝐸 𝐢 .

  • 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

Q10:

In the figure, π‘Ÿ = 5 0 c m , 𝐴 𝐡 = 9 7 c m , and 𝐢 𝐷 = 1 0 9 c m . Find the perimeter and the area of 𝐴 𝐡 𝐢 𝐷 .

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

Q11:

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

  • Atrue
  • Bfalse

Q12:

Find the perimeter of the β–³ 𝐴 𝐡 𝐢 .

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