Quant Question Of The Day: 94
Geometry
Let ABC be a triangle such that AB=3, BC=4, and AC=5. Let X be a point in the triangle. Compute the minimal possible value of AX²+BX²+CX².
AX2 + BX2 + CX2 = p2 + q2 + ( 3-p)2 + (4-q)2 + p2 + q2
3 ( q – 4/3)2 + 3 ( p -1)2 + 50/3
Minimum AX2 + BX2 + CX2 = 50/3
18.75
50/3
17
A. 75/4
Sir, why can’t we consider X to be the incentre? In that case the value would come out to be 17