Circles distance I

In an isosceles triangle ABC, we draw the circumscribed circle $C_1$ with center $O_1$ and the inscribed circle $C_2$ with centre $O_2$.

If AB = 520, AC = 520 and BC = 624, the distance $O_1{O}_2$ is the integer 65.

How many isosceles integer triangles with perimeter $\le {10}^8$ are there such as the distance $O_1{O}_2$ is an integer .

Answer format: the count

Hint: you are given 469 for a perimeter of ${10}^4$

[My timing: < 90 sec]