Problem

Problem

If Δ0\Delta_0 is the area of Δ\Delta formed by joining the points of contact of incircle with the sides of the given triangle whose area is Δ\Delta. Similarly Δ1,Δ2\Delta_1, \Delta_2 and Δ3\Delta_3 are the corresponding area of the Δ\Delta formed by joining the points of contact of excircles with the sides. Prove that Δ1Δ+Δ2Δ+Δ3Δ−Δ0Δ=2\frac{\Delta_1}{\Delta} + \frac{\Delta_2}{\Delta} + \frac{\Delta_3}{\Delta} - \frac{\Delta_0}{\Delta} = 2

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