Question

how to find arbitrary point in mean​

Answer 1

Answer:

an arbitrary point P is chosen on side BC of triangle ABC and perpendiculars PU and PV are drawn from P to other two sides of the triangle. (It may be that U or V lies on an extension of AB or AC and not on the actual side of the triangle. This can happen, for instance, if angle A is obtuse and point P is very near B or C.) Show that the sum PU+PV of the lengths of the two perpendiculars is constant as P moves along BC. In other words, this quantity is independent of the choice of P.