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Prove that if for {a, b, c} R and all n N there exists

a triangle with the sides an, bn and cn, then all of these triangles

are isoscoles.

Problem 2

A circle with a radius of 6.25 is circumscribed around a triangle

with the sides a, b and c. Find these sides, if {a, b, c} N.

Problem 3

A line splits a triangle into two new figures with equal perimeters

and areas. Prove that the center of the inscribed circle lies on this line.

Problem 4

The eight lines that connect the vertices of a parallelogram with the

centers of the two opposite sides form an octogon. Prove that the

octogon's area is exactly one sixth the area of the parallelogram

please guys I'm a new member here can you help me in these geometry problems?