2006 Seniors Pancyprian/2nd grade/Problem 4

Problem

A quadrilateral $\alpha \beta \gamma \delta$ , that has no parallel sides, is inscribed in a circle, its sides $\delta \alpha$ , $\gamma \beta$ meet at $\epsilon$ and its sides $\beta\alpha$ , $\gamma\delta$ meet at $\zeta$ . If the bisectors of of $\angle\delta\epsilon\gamma$ and $\angle\gamma\zeta\beta$ intersect the sides of the quadrilateral at the points $\kappa, \lambda, \mu, \nu$ prove that

i)the bisectors intersect normally

ii)the points $\kappa, \lambda, \mu, \nu$ are vertices of a rhombus.

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2006 Seniors Pancyprian/2nd grade/Problem 4

Problem

Solution

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