MathDB

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

Source:

June 23, 2012

geometryincenterTriangle

Problem Statement

Consider an acute angled triangle

PQR

such that

C,I

and

O

are the circumcentre, incentre and orthocentre respectively. Suppose

\angle QCR, \angle QIR

and

\angle QOR

, measured in degrees, are

\alpha, \beta

and

\gamma

respectively. Show that

\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}>\frac{1}{45}