# Geometry

#### Triagle Formulas

Right triangle formulas: $\qquad \qquad c^2 = a^2 + b^2 \qquad \qquad \qquad S = \frac{1}{2}ab = \frac{1}{2}ch_c \qquad \qquad a^2 = a_1c \qquad \qquad \qquad b^2 = b_1c$
$h_c^2 = a_1.b_1 \qquad \qquad \qquad r = \frac{a + b - c}{2} \qquad \qquad \qquad \textrm{ sin }\alpha = \frac{a}{c} \qquad \qquad \qquad \textrm{ cos }\alpha = \frac{b}{c} \qquad \qquad \qquad \textrm{ tg }\alpha = \frac{a}{b} \qquad \qquad \qquad \textrm{ cotg }\alpha = \frac{b}{a}$
Triangle formulas: $x \textrm{ , } y \qquad a \ne 0 \qquad b \ne 0$
$a^2 = a^2 + b^2 - 2ab \textrm{ cos } \gamma \qquad \qquad \qquad \qquad \qquad \frac{a}{\textrm{ sin } \alpha} = \frac{b}{\textrm{ sin } \beta} = \frac{c}{\textrm{ sin } \gamma} = 2R$
Median formulas: $m_a^2 = \frac{1}{4}( 2b^2 + 2c^2 - a^2 ) \qquad \qquad m_b^2 = \frac{1}{4}( 2a^2 + 2c^2 - b^2 ) \qquad \qquad m_c^2 = \frac{1}{4}( 2a^2 + 2b^2 - c^2 )$
Bisector formulas: $\qquad \qquad \frac{a}{b} = \frac{n}{m} \qquad \qquad \qquad \qquad l_c^2 = ab - nm$

#### Area Formulas

Area of a triagle: $\qquad \qquad \qquad S = \frac{1}{2}ch_c \qquad \qquad \qquad S = \frac{1}{2}ab \textrm{ sin } \gamma \qquad \qquad S = \sqrt{p(p - a)(p - b)(p - c)} \\ \qquad \qquad \qquad S = pr \qquad \qquad \qquad \qquad S = \frac{abc}{4R}$
Area of a parallelogram: $\qquad S = ah_a \qquad \qquad S = ab \textrm{ sin } \alpha$
Area of a rectangle: $\qquad S = \frac{1}{2}d_1d_2 \textrm{ sin } \phi$
Area of a prescribed polygon: $\qquad S = pr$

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