TR-MO-R1 2016 Problem 17

Dar açılı bir $ABC$ üçgeninin $AD$ kenarortayı, $BE$ yüksekliği ve $CF$ iç açıortayı noktadaştır. $|BC| = 10$ , $|CA| = 6$ ise $|AB|$ kaçtır?

a) $4\sqrt{5}$ b) $9$ c) $\sqrt{85}$ d) $3\sqrt{10}$ e) $\sqrt{91}$

Official text Turkish Mathematical Olympiad, first round 2016 official paper, page 7. Quoted with source.

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