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17

Part of 1995 Baltic Way

Problems(1)

Exists alpha for inequality with median and altitude

Source: Baltic Way 1995

10/8/2011
Prove that there exists a number α\alpha such that for any triangle ABCABC the inequality max⁡(hA,hB,hC)≤α⋅min⁡(mA,mB,mC) \max(h_A,h_B,h_C)\le \alpha\cdot\min(m_A,m_B,m_C) where hA,hB,hCh_A,h_B,h_C denote the lengths of the altitudes and mA,mB,mCm_A,m_B,m_C denote the lengths of the medians. Find the smallest possible value of α\alpha.
inequalitiesgeometry proposedgeometry