Если правильно поняты координаты точки Е((3-√3)/2; (√3-1)/2), то обозначим С = А, В = Д и С = Е
A(xA; yA) = A(0; -1)
B(xB; yB) = B(1; 0)
C(xC; yC) = C(0.63397; 0.36603)
I) Найдем длины сторон:
AB = <span>√(<span>(xB - xA)</span></span><span>²</span><span> + (yB - yA)</span>²)<span> </span><span>=</span><span> </span><span>√((1 - 0)</span>²<span> + (0 - (-1))</span>²)<span> </span><span>=</span><span> </span><span>√(1</span>²<span> + 1</span>²)<span> </span><span>=</span><span> </span><span>√(1 + 1)</span><span> </span><span>=</span><span> </span><span>√2</span><span> </span><span>= 1,414.</span>
AC = <span>√(<span>(xC - xA)</span></span>²<span><span> + (yC - yA)</span></span>²) = <span>√(<span>(0,63397 - 0)</span></span>²<span><span> + (0,36603 - (-1))</span></span>²) =<span>√(<span>0,63397</span></span>²<span><span> + 1,36603</span></span>²) = <span>√(0,40192 + 1,86602)</span>= <span>√2,26795</span> = 1,506.
BC = <span>√(<span>(xC - xB)</span></span>²<span><span> + (yC - yB)</span></span>²) =<span>√<span>(0,63397 - 1)</span></span>²<span><span> + (0,36603 - 0)</span></span>²<span> = </span>√(<span>(-0,36603)</span>²<span> + 0,36603</span>²) = <span>√(0,13397 + 0,13397)</span> =<span>√0,26795</span> = 0,518.
Периметр: P = AB + AC + BC = 1,414 + 1,506 + 0,518 = 3,438.
<span><span><span>Полупериметр: p = </span>P/2 = 3,438/2 = 1,719</span><span>22.</span></span>
II) Найдем площадь:
<span><span><span>S = (</span>1/2)*<span>|(xB - xA)(yC - yA) - (xC - xA)(yB - yA)| </span></span></span><span><span> = (1/2)*|(1 - 0)(0,36603 - (-1)) - (0,63397 - 0)(0 - (-1))| </span></span><span><span> = (1/2) |1 ∙ 1,36603 - 0,63397 ∙ 1| = (1/2) |1,366 - 0,634| = |0,73205|/2 = 0,366</span><span>025.</span></span>
III) Найдем параметры вписанной окружности:
<span><span><span>Радиус r = </span>S/р = 0,366025/1,71922 = 0,21294.</span></span>
