All formulas for radius of a circumscribed circle.

Radius of the circumcircle of a triangle

a , b , c blue    -  sides of a triangle

s12 black  - semiperimeter    

s (abc)2

O black  - circumcenter    

 

Calculate the radius of the circumcircle of a triangle if given all three sides ( R  ) :

radius circumscribed circle triangle F

 

 

Radius of the circumscribed circle of an equilateral triangle

radius circumscribed circle equilateral triangle

a12 blue    -  side of a triangle

h  - height    

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of an equilateral triangle if given side or height ( R  ) :

radius circumscribed circle equilateral triangle F1     radius circumscribed circle equilateral triangle F2

 

 

Radius of the circumscribed circle of an isosceles triangle

radius circumscribed circle isosceles triangle

a12 green    - equal sides of a triangle

b blue  - side  (base)  

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of an isosceles triangle if given sides ( R  ) :

radius circumscribed circle isosceles triangle F

 

 

Radius of the circumscribed circle of a right triangle

radius circumscribed circle right triangle

a12 green , b   -  legs of a right triangle

c blue  - hypotenuse    

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of a right triangle if given legs or hypotenuse ( R  ) :

radius circumscribed circle right triangle F

 

 

Radius of the circumscribed circle of a rectangle

radius circumscribed circle rectangle

a12 green ,  b  -  sides of a rectangle

d blue1  - diagonal    

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of a rectangle if given sides or diagonal ( R  ) :

radius circumscribed circle rectangle F

 

 

Radius of the circumcircle of a regular hexagon

radius circumscribed circle regular hexagon

 

a12 green    - equal sides of a hexagon

d blue1  - diagonal    

O black  - circumcenter    

 

Calculate the radius of the circumcircle of a regular hexagon if given side or diagonal ( R  ) :

radius circumscribed circle regular hexagon F

 

 

Radius of the circumscribed circle of a square

radius circumscribed circle square

a12 green   -  side of a square

d blue1  - diagonal    

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of a square if given side or diagonal ( R  ) :

radius circumscribed circle square F

 

 

Radius of the circumscribed circle of an isosceles trapezoid

radius circumscribed circle isosceles trapezoid

a12 green    - equal sides of a trapezoid

b brown ,  c orange  - bases

d blue1  - diagonal    

s (abc)2 orange

s (abc)2 brawn

O black  - circumcenter    

Calculate the radius of the circumcircle of an isosceles trapezoid if given sides and diagonal ( R  ) :

radius circumscribed circle isosceles trapezoid F5

radius circumscribed circle isosceles trapezoid F6

 

 

Radius of the circumscribed circle of a regular polygon

radius circumscribed circle regular polygon

a12 green  -  side  of a polygon

n black  -  number  of sides

O black  - circumcenter    

 

 

Calculate the radius of the circumcircle of a regular polygon if given side and number of sides ( R  ) :

radius circumscribed circle regular polygon F