Radius of a circle inscribed in a rhombus

Details
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