#### UK

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Let $ABCD$ be an cyclic quadrilateral and let $HA, HB, HC, HD$ be the orthocentres of triangles $BCD, CDA, DAB$, and ABC respectively. Prove that the quadrilaterals $ABCD$ and $H_AH_BH_CH_D$ are congruent.

Solve in positive integers $\big(1+\frac{1}{x}\big)\big(1+\frac{1}{y}\big)\big(1+\frac{1}{z}\big)=2$

Calculate the value of $$\dfrac{2014^4+4 \times 2013^4}{2013^2+4027^2}-\dfrac{2012^4+4 \times 2013^4}{2013^2+4025^2}$$