MathDB

P33 [Geometry] - Turkish NMO 1st Round - 2003

Source:

May 31, 2014

geometryincenter

Problem Statement

Let

G

be the intersection of medians of

\triangle ABC

and

I

be the incenter of

\triangle ABC

. If

|AB|=c

,

|AC|=b

and

GI \perp BC

, what is

|BC|

?

<span class='latex-bold'>(A)</span>\ \dfrac{b+c}2 \qquad<span class='latex-bold'>(B)</span>\ \dfrac{b+c}{3} \qquad<span class='latex-bold'>(C)</span>\ \dfrac{\sqrt{b^2+c^2}}{2} \qquad<span class='latex-bold'>(D)</span>\ \dfrac{\sqrt{b^2+c^2}}{3\sqrt 2} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}

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