It is the Pythagoras' theorem that states for any right angle triangle:-
a2+b2 = c2 whereas a and b are its sides with c being its hypotenuse
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The Pythagorean Theorem is not a triangle. It's a statement that describes a relationship among the lengths of the sides in any right triangle.
The circumcenter of a triangle is equidistant from the vertices of a triangle.
Yes
A right angle triangle
You use Lami's theorem wen you triangle of forces to calculate the sides of the triangle or the angles opposite to a side.