Teaser 2922: Inscribed

From The Sunday Times, 23rd September 2018 [link]

The Republic of Mathematica has an unusual rectangular flag. It measures 120 cm by 60 cm and has a red background. It features a green triangle and a white circle. All the lengths of the sides of the triangle and the radius of the circle (which touches all three sides of the triangle) are whole numbers of cm. Also, the distances from the vertices of the triangle to the centre of the circle are whole numbers of cm. The flag has a line of symmetry.

What is the length of the shortest side of the triangle?

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