64. To a circle of radius $R$ from an external point $M$, tangents $M A$ and $M B$ are drawn, forming an angle $\alpha$. Determine the area of the figure bounded by the tangents and the smaller arc of the circle.
64. $R^{2}\left[\operatorname{ctg} \frac{\alpha}{2}-\frac{1}{2}(\pi-\alpha)\right]$. 65. $\frac{a}{4} \sqrt{10}$. 66. $\frac{a\left(4 \sin ^{2} \alpha+1\right)}{8 \sin \alpha}$. 67. $2 r^{2}(2 \sqrt{\overline{3}}+3)$. 68. $\frac{a^{2}+4 r^{2}}{4 r}$, 69. $\frac{3 a}{2(5+\sqrt{13})}$, 70. $\frac{a \sqrt[V]{10}}{4}$. 71. 2. 72. $\frac{a^{8 b}}{4\left(a^{2}+b^{2}\right)}$. 73. $\frac{a}{2}\left(\operatorname{tg} \frac{\alpha}{2}-\operatorname{ctg} \alpha\right)$. 74. $\frac{a \cos \frac{\alpha-\beta}{2}}{\sin (\alpha+\beta)}$. 75. $\frac{R^{2}-a^{2}}{2 R}$. 76. $\frac{a \sqrt{\overline{7}}}{3 \sqrt{3}}$. 77. $a\left(\frac{\sqrt{\overline{3}}}{3}+\frac{1}{2}\right) \cdot$ 78. $\frac{a^{2} \sqrt{\overline{3}}}{12}$. 79. $\frac{1}{2} \times$ $\times(\gamma+\beta-\alpha)$. 80. $\frac{a c+b d}{a}$. 81. $\frac{\pi}{2 \sin ^{2} \alpha \sin 2 \beta}$. 82. $\frac{|b-a|}{4} \times$ $\times \sqrt{4 d^{2}-(b-a)^{2}} \cdot 83.2\left(R^{2}+a^{2}\right)$.