1)The perimeter of triangle ABC is 18, its angles A and B are related by the relation: 2(cosA + cosB) = 3+2cos(A+B).

Find the area of the triangle whose sides are equal to the bisectors of triangle ABC.

2)The area of the triangle is 50, and the sum of the squares of the two sides of the triangle is 200. Find the perimeter of the triangle.

3)In this triangle, the angle between the two medians is equal to the smallest positive root of the equation: 2cosxcos((16x+1620)/6)=sin(8x/3), and the lengths of the medians are a and b respectively. Find the radius of the circle whose area is equal to the area of the triangle.

If the 2nd problem is basically clear to me...

Then by 1 and 3 tasks no thoughts! Can you at least give me a hint where to start???

Nice problem! I like to decide such ones

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