MathDB

2

Part of 1985 Iran MO (2nd round)

Problems(2)

Plot the triangle - [Iran Second Round 1985]

Source:

12/29/2010
In the triangle ABCABC the length of side ABAB, and height AHAH are known. also we know that ∠B=2∠C.\angle B = 2 \angle C. Plot this triangle.
geometry proposedgeometry
Find the value od the fraction - [Iran Second Round 1985]

Source:

12/28/2010
Let x,yx, y and zz be three positive real numbers for which x2+y2+z2=xy+yz+zx.x^2+y^2+z^2=xy+yz+zx. Find the value of xx+y+z.\frac{\sqrt x}{\sqrt x + \sqrt y+ \sqrt z}.
algebra proposedalgebra