Solve this given problem:

Dear Student,
Given,

∠ BAE = 90 ° - B ∠ ABF = 90 ° - A ∴ ∠ AHB = A + B Similarly, ∠ BHC = B + C and ∠ AHC = A + C Let R be the circumcircle of △ ABC and R_{1}, R_{2} and R_{3} be the radii of the circumcircles of △ AHB, △ BHC and △ AHC, respectively . In △ AHB, ∠ AHB = A + B ∴ R_{1} = \frac{AB}{2 \sin (A + B)} = \frac{c}{2 sinC} = R Similarl y, R_{2} = R and R_{3} = R

Thus Correct Option (A)

Regards