Such an unbalanced kata:

• performance criteria not mentioned in description
• random tests immediately deal with huge numbers
• in javascript, numbers go way beyond max safe integer, rendering most solutions incompatible with ref solution

Fun kata, thank you. Suggest to fix a couple of typos in the description: diametr -> diameter and quadrilaterlas -> quadrilaterals. Also combinations is not the best function name in Python because it clashes with itertools.combinations.

i think that i concidered all the possible combinations:
*for triangles:
1.two points on arc and one point on diameter
2.two points on diameter and one point on arc
3.three points on arc
*for quadrilaterals:
1.two points on diameter and two points on arc
2.one point on diameter and three points on arc
3.four points on arc

this passes eleven tests but no more. do i miss out anything?

Just to make it clear: is it OK if a triangle or a quadrilateral is built on points located solely on arc?