Prove that an infinite number of triangles can be inscribed in the hyperbola xy=c^2 whose sides touch the parabola y^2=4ax.
87206
Prove that a triangle can be inscribed in the hyperbola $xy=c^2$ whose sides touch the parabola $y^2=4ax$.
17264
Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
37744
Prove that given $a,b,c > 0$, it is possible to construct a triangle with sides of length $a,b,c$ if and only if $pa^2+qb^2 > pqc^2$
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
103116
Prove that any odd number can be a leg in a Pythagorean Triple
79777
An olympiad Geometry problem involving triangles
56320
Prove that the circumradius of $\triangle PAB$ is constant
152167
Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
123133
If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP
61343
Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
90056
A synthetic geometrical proof required on a result regarding Isosceles triangles.
81975
Sequence of triangles with exponentiated sides
130436
bisectors of an angle in a triangle intersect at a single point - proof verification
54170
Prove that $\triangle ABC$ is equilateral, If $(a+b-c)^{a}\cdot (b+c-a)^{b}\cdot (c+a-b)^{c}\geq a^a\cdot b^b\cdot c^c$
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
131736
Proving a triangle with different edge colors exists in a graph.