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For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

Polygons and Circles

Samdom For Peace Welcome to our site.
I greet you this day,
The polygons discussed in this site are regular polygons only.
First: read the notes. Second: view the videos. Third: solve the questions/solved examples. Fourth: check your solutions with my thoroughly-explained solutions. Fifth: check your answers with the calculators as applicable.
I wrote the codes for the calculators using JavaScript, a client-side scripting language. Please use the latest Internet browsers. The calculators should work. Only integers and decimals are allowed. Fractions are not allowed.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me. If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting!!!

Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

Equilateral Triangle and Circle

Equilateral Triangle inscribed in a Circle OR a Circle circumscribed about an Equilateral Triangle

Formulas

$ h = \dfrac{3r}{2} \\[5ex] b = r\sqrt{3} \\[3ex] a = \dfrac{r}{2} \\[5ex] r = 2a \\[3ex] A_T = \dfrac{bh}{2} \\[5ex] A_C = \pi r^2 \\[3ex] \dfrac{A_T}{A_C} = \dfrac{3\sqrt{3}}{4\pi} \\[5ex] \dfrac{A_C}{A_T} = \dfrac{4\pi \sqrt{3}}{9} \\[5ex] A_r = A_C - A_T \\[3ex] A_{ep} = \dfrac{A_r}{3} $ $ h = \dfrac{b\sqrt{3}}{2} \\[5ex] b = \dfrac{2h\sqrt{3}}{3} \\[5ex] a = \dfrac{b\sqrt{3}}{6} \\[5ex] r = \dfrac{2h}{3} \\[5ex] A_T = \dfrac{3r^2\sqrt{3}}{4} \\[5ex] $ $ h = 3a \\[3ex] b = 2a\sqrt{3} \\[3ex] a = \dfrac{h}{3} \\[5ex] r = \dfrac{b\sqrt{3}}{3} \\[5ex] $

Calculators

  • Equilateral Triangle inscribed in Circle

Given: radius of the circle

To find: other details

  • Equilateral Triangle inscribed in Circle

Given: perpendicular height of the equilateral triangle

To find: other details

  • Equilateral Triangle inscribed in Circle

Given: base of the triangle (or any side)

To find: other details

  • Equilateral Triangle inscribed in Circle

Given: apothem of the triangle

To find: other details

Circle inscribed in an Equilateral Triangle OR an Equilateral Triangle circumscribed about a Circle

Formulas

$ h = 3r \\[3ex] b = 2r\sqrt{3} \\[3ex] a = r \\[3ex] r = a \\[3ex] A_T = \dfrac{bh}{2} \\[5ex] A_C = \pi r^2 \\[3ex] \dfrac{A_T}{A_C} = \dfrac{3\sqrt{3}}{\pi} \\[5ex] \dfrac{A_C}{A_T} = \dfrac{\pi \sqrt{3}}{9} \\[5ex] A_r = A_T - A_C \\[3ex] A_{ep} = \dfrac{A_r}{3} $ $ h = \dfrac{b\sqrt{3}}{2} \\[5ex] b = \dfrac{2h\sqrt{3}}{3} \\[5ex] a = \dfrac{b\sqrt{3}}{6} \\[5ex] r = \dfrac{h}{3} \\[5ex] A_T = 3r^2\sqrt{3} \\[3ex] $ $ h = 3a \\[3ex] b = 2a\sqrt{3} \\[3ex] a = \dfrac{h}{3} \\[5ex] r = \dfrac{b\sqrt{3}}{6} \\[5ex] $

Calculators

  • Circle inscribed in Equilateral Triangle

Given: radius of the circle

To find: other details

  • Circle inscribed in Equilateral Triangle

Given: perpendicular height of the equilateral triangle

To find: other details

  • Circle inscribed in Equilateral Triangle

Given: base of the triangle (or any side)

To find: other details

  • Circle inscribed in Equilateral Triangle

Given: apothem of the triangle

To find: other details

Square and Circle

Square inscribed in a Circle OR a Circle circumscribed about a Square

The diameter of the circle is equal to the diagonal of the square

Formulas

$ d = d_S \\[3ex] l = r\sqrt{2} \\[3ex] a = \dfrac{l}{2} \\[5ex] r = \dfrac{l\sqrt{2}}{2} \\[5ex] A_S = l^2 \\[3ex] A_C = \pi r^2 \\[3ex] \dfrac{A_S}{A_C} = \dfrac{2}{\pi} \\[5ex] \dfrac{A_C}{A_S} = \dfrac{\pi}{2} \\[5ex] A_r = A_C - A_S \\[3ex] A_{ep} = \dfrac{A_r}{4} $ $ l = 2a \\[3ex] a = \dfrac{r\sqrt{2}}{2} \\[5ex] r = a\sqrt{2} \\[3ex] A_S = 2r^2 \\[3ex] $

Calculators

  • Square inscribed in Circle

Given: radius of the circle

To find: other details

  • Square inscribed in Circle

Given: side length of the square

To find: other details

  • Square inscribed in Circle

Given: apothem of the square

To find: other details

Circle inscribed in a Square OR a Square circumscribed about a Circle

Formulas

Calculators

  • Circle inscribed in Square

Given: radius of the circle

To find: other details

  • Circle inscribed in Square

Given: side length of the square

To find: other details

  • Circle inscribed in Square

Given: apothem of the square

To find: other details