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Explanation:

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Concept: Diameter of a circle makes an angle of 90° on the circle.

∴ (2r)² = a² + b² 
⇒ 4r² = a² + b² 

Now, Area of the triangle = 1/2 × base × height
= 1/2 × a × b
= $\frac{\mathrm{ab}({\mathrm{a}}^2+{\mathrm{b}}^2)}{2({\mathrm{a}}^2+{\mathrm{b}}^2)}$
= $\frac{\mathrm{ab}\times 4{\mathrm{r}}^2}{2({\mathrm{a}}^2+{\mathrm{b}}^2)}$
= $\frac{2{\mathrm{abr}}^2}{{\mathrm{a}}^2+{\mathrm{b}}^2}$

Hence, option (a).​​​​​​​$$