1the \ height \ of \ the \ triangle \ is \ fixed \ that \ is \ 1 \\ hence \ area \ is \\ {\color{red} \frac{x}{2} } \ \ \ \ \ where \ x =PQ \\ now \ \triangle =\frac{xyz}{4R} \\ \frac{x}{2}=\frac{xyz}{4R}\\ y=QR ,z=PR\\ R=\frac{yz}{2} \\ now \\ PR_{max}=\sqrt{2} \\ QR_{max}=\sqrt{2} \\ hence \\ R_{max}=1 \\ PR_{min} =1 \\ QR_{min} =1 \\ R_{min}=\frac{1}{2} \\ R\in (\frac{1}{2},1)
