Math Formulas Search

1.

Sum of opposite angles

$\alpha + \gamma = 180\degree$

2.

Sum of opposite angles

$\beta + \gamma = 180\degree$

3.

Ptolemy's theorem

$ac+bd=d_1d_2$

4.

Permeter

$P = a+ b+ c+ d$

5.

Circumscribed radius

$R=\dfrac{1}{4} \sqrt{ \dfrac{(ac+bd)(ad+bc)(ab+cd)}{(p-a)(p-b)(p-c)(p-d)} }, \text{ where } p = \dfrac{a+b+c+d}{2}$

6.

Area

$A = \dfrac{1}{2} d_1d_2 \sin \psi$

7.

Area

$A = \sqrt{(p-a)(p-b)(p-c)(p-d)}, \text{ where } p=\dfrac{a+b+c+d}{2}$

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