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Let $$\triangle ABC$$ be a right triangle with right angle at $$C$$. Suppose this right triangle has legs $$BC=a$$, $$AC=b$$, hypotenuse $$AB=C$$, and circumradius $$R$$. Two copies of this triangle can be joined to form an isosceles triangle in two ways. With $$a$$ as a common side, you can form an isosceles triangle with sides $$c,c,2b$$ and circumradius $$R_1$$. With $$b$$ as a common side, you can form an isosceles triangle with sides $$c,c,2a$$ and circumradius $$R_2$$. Find a formula relating $$R,R_1,R_2$$.