Thread: Rhombus problem

I'm stuck on how to even begin the following problem. Any tips or suggestions would be greatly appreciated.

Rhombus ABCD has diagonals 40 and 42. Prove that the sum of the distances of any of its interior points to sides AB, BC, CD and DA is a constant and find its value.

Originally Posted by kwilki1

I'm stuck on how to even begin the following problem. Any tips or suggestions would be greatly appreciated.

Rhombus ABCD has diagonals 40 and 42. Prove that the sum of the distances of any of its interior points to sides AB, BC, CD and DA is a constant and find its value.

Did you make a sketch?

Since opposite sides are parallel the perpendicular distance between opposite sides is constant.

That means you only have to determine the perpendicular distance between the opposite sides.