Suppose angle TIP and angle TOP are isosceles triangles. Also suppose that TI = 5, PI = 7, and PO = 11.
What is the sum of all possible lengths for TP?
So, TIP is a triangle with side lengths 5, 7, and x, an array of values the missing side lengths could be. Since TIP is a isosceles triangle, I know that the third side length is 5 or 7. Therefore, the answer to your problem is 12, since the sum of x is 5 + 7.