Problem #PRU-66991

Problem

Michael used different numbers \(\{0,1,2,3,4,5,6,7,8,9\}\) to put in the circles in the picture below, without using any one of them twice. Inside each triangle he wrote down either the sum or the product of the numbers at its vertices. Then he erased the numbers in the circles. Which numbers need to be written in circles so that the condition is satisfied?