40. Find the length of a segment of a line parallel to the bases of a trapezoid and passing through the point of intersection of the diagonals, if the bases of the trapezoid are equal to $a$ and $b$.
40. $\frac{2 a b}{a+b}$. 41. $\arccos \frac{1-k}{1+k}$. 42. $\frac{a+b}{4} \sqrt{3 b^{2}+2 a b-a^{2}}$. 43. $a^{2}$. 44. $\frac{1}{2} \sqrt{\frac{S}{2}} \cdot$ 45. $\left(\sqrt{S_{1}}+V \overline{S_{2}}\right)^{2} \cdot 46.90^{\circ}+\frac{\alpha}{2} \cdot 47 . \frac{|a-b|}{a+b} \times$ $\times \sqrt{a^{2}+b^{2}} .48 . \arcsin \left(1-\frac{a}{b}\right) \cdot 49 .(6-\pi): 2 \pi:(6-\pi) \cdot 50 \cdot \frac{a^{2}}{8} \times$ $\times(\sqrt{2}-1)[(2 \sqrt{2}-1) \pi-4]$. 51. $\frac{a^{2}}{4}(6 \sqrt{\overline{3}}-6-\pi)$. 52. $\frac{R^{2}}{2} \times$ $\times\left(\frac{\pi}{3}+\frac{\sqrt{ } \overline{3}}{2}\right)$. 53. $\frac{1}{2} V \overline{b^{2}-a^{2}}$. 54. $\frac{d}{3}$. 55. $\frac{4}{9}$ S. 58. If $\alpha90^{\circ}, \beta90^{\circ}, \quad$ then $\quad 90^{\circ}+\alpha, \quad \beta-90^{\circ}, \quad 180^{\circ}-\alpha-\beta$. 59. ${ }_{2}^{1} \sqrt{m^{2}-4 S}, \quad 60 \cdot \frac{a}{5}, 61 \cdot \frac{36}{25} h^{2} \cdot 62 . \sqrt{\frac{S}{\pi\left(4 \pi^{2}-1\right)}}$.