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2

Part of 1997 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 1997 Day 1 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 1997

9/20/2018
In isosceles triangle ABCABC with base side ABAB, on side BCBC it is given point MM. Let OO be a circumcenter and SS incenter of triangle ABCABC. Prove that SM∣∣AC⇔OM⊥BS SM \mid \mid AC \Leftrightarrow OM \perp BS
geometrycircumcircleincenterAngle Chasingcyclic quadrilateral