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Romanian TST 1993

Source: Romanian TST 1993 - Day 1 - Problem 2

April 9, 2012
geometry proposedgeometry

Problem Statement

Let ABCABC be a triangle inscribed in the circle C(O,R)\mathcal{C}(O,R) and circumscribed to the circle C(L,r)\mathcal{C}(L,r). Denote d=RrR+rd=\dfrac{Rr}{R+r}. Show that there exists a triangle DEFDEF such that for any interior point MM in ABCABC there exists a point XX on the sides of DEFDEF such that MX≤dMX\le d.
Dan Brânzei
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