All formulas for radius of a circle inscribed

Radius of a circle inscribed in a triangle

radius circle inscribed triangle

a12 blue , b blue , c blue    -  sides of a triangle

s12 black  - semiperimeter    

s (abc)2 blue

O black  - circumcenter    

 

Calculate the radius of a inscribed circle of a triangle if given all three sides ( r  ) :

radius circle inscribed triangle F

 

 

Radius of a circle inscribed in an equilateral triangle

radius circle inscribed equilateral triangle

 

a12 blue    - equal sides of a triangle

O black  - circumcenter    

 

 

Calculate the radius of a inscribed circle of an equilateral triangle if given side ( r  ) :

radius circle inscribed equilateral triangle F

 

 

Radius of a circle inscribed in an isosceles triangle

1.  Find radius of a circle inscribed if you know side and angle at the base

 

radius circle inscribed isosceles triangle

a12 blue    - equal sides of a triangle

b blue  - side  (base)  

alpha-angle  - angle  at the base

O black  - circumcenter    

 

Calculate the radius of a circle inscribed in an isosceles triangle if given sides ( r  ) :

radius circle inscribed isosceles triangle F

 

Calculate the radius of a circle inscribed in an isosceles triangle if given side and angle ( r  ) :

radius circle inscribed isosceles triangle Formula

radius circle inscribed isosceles triangle Formula1

 

 

2.  Find radius of a circle inscribed if you know side and height

 

radius circle inscribed isosceles triangle1

a12 blue    - equal sides of a triangle

b blue  - side  (base)  

h-height  - height

O black  - circumcenter    

 

Calculate the radius of a circle inscribed in an isosceles triangle if given side and height ( r  ) :

radius circle inscribed isosceles triangle Formula h

radius circle inscribed isosceles triangle Formula1 h

 

 

Radius of a circle inscribed in a right triangle

radius circle inscribed right triangle

 

a12 blue , b blue   -  legs of a right triangle

c blue  - hypotenuse    

O black  - circumcenter    

 

Calculate the radius of a inscribed circle of a right triangle if given legs and hypotenuse ( r  ) :

radius circle inscribed right triangle F

 

 

Radius of a circle inscribed in a square

radius circle inscribed square

 

a12 blue   -  side of a square

O black  - circumcenter    

 

 

Calculate the radius of a inscribed circle of a square if given side ( r  ) :

radius circle inscribed square F

 

 

Radius of a circle inscribed in a rhombus 

1.  The radius of a circle inscribed in a rhombus if you know diagonal, side and angle.  

radius circle inscribed rhombus d

 

DD blue , d blue   -  diagonals of a rhombus

a black  - side

angle alpha  - acute angle of a rhombus

O black  - circumcenter    

 

Calculate the radius of a inscribed circle of a rhombus if given diagonals ( r  ) :

radius circle inscribed rhombus d F

 

given side and angle ( r  ) :

radius circle inscribed rhombus Formula

 

given diagonal and angle ( r  ) :

radius circle inscribed rhombus Formula3

radius circle inscribed rhombus Formula4

 

given diagonal and side ( r  ) :

radius circle inscribed rhombus Formula1

radius circle inscribed rhombus Formula2

 

 

2.  The radius of a circle inscribed in a rhombus if you know height  

radius circle inscribed rhombus h

 

h   -  height of a rhombus

a black  - side  of a rhombus  

O black  - circumcenter    

 

Formula for calculating radius of a inscribed circle of a rhombus if given height ( r  ) :

radius circle inscribed rhombus h F

 

 

Radius of a circle inscribed in an isosceles trapezoid

radius circle inscribed trapezoid

a black  -  upper base

b black  -  lower base

h   -  height of a trapezoid

O black  - circumcenter    

 

Calculate the radius of a inscribed circle in an isosceles trapezoid if given height or bases ( r  ) :

radius circle inscribed trapezoid F

 

 

Radius of a circle inscribed in a regular polygon

radius circle inscribed regular polygon

 

a12 blue  -  side  of a polygon

N14 black  -  number  of sides

O black  - circumcenter    

 

Calculate the radius of a inscribed circle of a regular polygon if given side and number of sides ( r  ) :

radius circle inscribed regular polygon F

 

 

Radius of a circle inscribed in a regular hexagon

radius circle inscribed regular hexagon

 

a12 blue    - equal sides of a hexagon

O black  - circumcenter    

 

 

Formula for calculating radius of a inscribed circle of a regular hexagon if given side ( r  ) :

radius circle inscribed regular hexagon F