Solve .41421<a<2,quadb=sqrt{4-a^{2}},quadc=sqrt{(asqrt{4-a^2}-2)^2}+sqrt{(sqrt{4-a^2}a+2)^2}

$$.41421 < a < 2 , \quad b = \sqrt { 4 - a ^ { 2 } } , \quad c = \sqrt { ( a \sqrt { 4 - a ^ { 2 } } - 2 ) ^ { 2 } } + \sqrt { ( \sqrt { 4 - a ^ { 2 } } a + 2 ) ^ { 2 } }$$

Solve for c

$$c=|a\sqrt{4-a^{2}}+2|+|a\sqrt{4-a^{2}}-2|$$

$$a>0.41421\text{ and }b=\sqrt{4-a^{2}}\text{ and }a<2$$

Solve for b

$$b=\sqrt{4-a^{2}}$$

$$c=4\text{ and }a<2\text{ and }a>0.41421$$