MathDB

5

Part of 2005 ISI B.Stat Entrance Exam

Problems(1)

sum of reciprocals of angles > 1/45 ....[ISI(BS) '05 #5]

Source:

6/23/2012
Consider an acute angled triangle PQRPQR such that C,IC,I and OO are the circumcentre, incentre and orthocentre respectively. Suppose ∠QCR,∠QIR\angle QCR, \angle QIR and ∠QOR\angle QOR, measured in degrees, are α,β\alpha, \beta and γ\gamma respectively. Show that 1α+1β+1γ>145\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}>\frac{1}{45}
geometryincenterTriangle