Geometry Level 4

A circle of radius t is tangent to hypotenuse, incircle and one leg of an isosceles right triangle with inradius $$r = 1 + sin\frac{\pi}{8}$$.

If the value of $$r \times t$$ can be written as $$\displaystyle \dfrac{a + \sqrt{a}}{b}$$

Where 'a' is square free & a,b are integers, find the value of $$a^{b} + b^{a}$$.

Try more from the set Radius Ratio

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