Recent content by klawesyn28

It's task from russian books with task from geometry. I don't see how your hints can help me.

why its circumradius OA_1 = 2?

Yes I started with this problem and then I don't know how to prove that when PA<=2, PB<=2, PC<=2, the circumradius is smaller than 2. P is point inside the triangle.

P is a point inside triangle ABC. In the triangle there is inscribed circle which radius is greater than 1. Prove that PA>2, PB>2 or PC>2. I don't know how to solve it. Could anybody help me?

The sphere is inscribed, it is inside the tetrahedron. I don't understand your question.

There is ABCD tetrahedron with inscribed sphere. S is a center of the sphere, radius of the sphere equates 1 and SA>=SB>=SC. Prove that SA>(5)^(0,5). I can't solve it. Could anybody help me?

I think that the answer is 4^5 but i don't know how to prove it.

I don't know how to solve this task: Participants of math competition are solving six tasks. For each task you can get one of marks - 6,5, 3 or 0 . It transpired that for each pair of participants we can indicate two tasks , that in each of them participant A got different mark from...