Lassen wir X=a (cos(t),sin(t)) im Abstand a um A(0,0) kreisen,
im Punkt Xt=F ist FA ⊥ FC, also FA FC =0
\(\small a \; \left(\begin{array}{r}\operatorname{cos} \left( t \right)\\\operatorname{sin} \left( t \right)\\\end{array}\right) \; \left(\left(\begin{array}{r}c\\b\\\end{array}\right) - a \; \left(\begin{array}{r}\operatorname{cos} \left( t \right)\\\operatorname{sin} \left( t \right)\\\end{array}\right) \right) = 0\)
===>
\(\small t= 2 \; \operatorname{tan⁻^1} \left( \frac{-\sqrt{-a^{2} + b^{2} + c^{2}} + b}{a + c} \right)\)
\(\small X_t=F=\left(a \; \operatorname{cos} \left( 2 \; \operatorname{tan⁻^1} \left( \frac{-\sqrt{-a^{2} + b^{2} + c^{2}} + b}{a + c} \right) \right), a \; \operatorname{sin} \left( 2 \; \operatorname{tan⁻^1} \left( \frac{-\sqrt{-a^{2} + b^{2} + c^{2}} + b}{a + c} \right) \right) \right) \)
\(\small\varphi(a, b, c) \, := \, \operatorname{cos⁻^1} \left( \frac{X \; \left(1, 0 \right)}{\left|X\right| \; \left|\left(1, 0 \right)\right|} \right)= \, \left|2 \; \operatorname{tan⁻^1} \left( \frac{-\sqrt{-a^{2} + b^{2} + c^{2}} + b}{a + c} \right)\right|\)
{a=1.65, b=1.65, c=1.85}
φ(a,b,c)/pi*180=6.541
