The diagonal of the rhombus ABCD intersects at point O. a circle with center at point O and radius equal to 2

The diagonal of the rhombus ABCD intersects at point O. a circle with center at point O and radius equal to 2, touches the sides of the rhombus, and side DC – at point T. Calculate the length of the sides of the rhombus if ED = 1

Triangle ОDТ is rectangular, since ОT is the height and radius of the circle drawn to the point of tangency, then ОD ^ 2 = ОT ^ 2 + DТ ^ 2 = 4 + 1 = 5.

Triangles ODT and OCD are similar in acute angle, then:

DТ / ОD = ОD / СD.

СD = ОD ^ 2 / DТ = 5/1 = 5 cm.

Answer: The sides of the rhombus are 5 cm.