The two circles' radii are 10 cm and 25 cm, respectively. Find the radius of the circle, which has its circumference equal to the sum of the circumference of the two circles. Use 3.14 as the value of π.

Step 1: Calculate the circumference of the first circle. The formula for the circumference of a circle is 2πr. So, for the first circle, it would be 23.1410 = 62.8 cm.

Step 2: Calculate the circumference of the second circle. Using the same formula, the circumference of the second circle is 23.1425 = 157 cm.

Step 3: Add the circumferences of the two circles together. 62.8 cm + 157 cm = 219.8 cm.

Step 4: Set the sum of the circumferences equal to the circumference of the third circle. The formula for the circumference of a circle is 2πr, so 219.8 cm = 23.14r.

Step 5: Solve for r (the radius of the third circle). Divide both sides of the equation by 23.14 to isolate r. r = 219.8 cm / (23.14) = 35 cm.

So, the radius of the circle which has its circumference equal to the sum of the circumference of the two circles is 35 cm.