A circle is inscribed in a rhombus with a side of 20. Find the radius of the circle if the smaller

A circle is inscribed in a rhombus with a side of 20. Find the radius of the circle if the smaller diagonal of the rhombus is 24.

d1 = 24 – the smaller diagonal of the rhombus;
a = 20 – rhombus side.

Find what is half of the smaller diagonal:
24/2 = 12.

Let’s calculate half of the larger diagonal using the Pythagorean theorem:
20² = 12² + x²;
x² = 256;
x = 16.

Let us determine what the large diagonal of the rhombus is equal to:
d2 = 16 * 2 = 32.

Find the radius of the inscribed circle through the diagonals of the rhombus:
r = d1 * d2 / (4 * a);
r = 24 * 32 / (4 * 20) = 9.6.

Answer: the radius of a circle inscribed in a rhombus is 9.6.