The barycentric coordinates of a point P with respect to the non-collinear points A, B,C is given by P = (a:ß:y)ABc, where a +B +y = 1. The cevian from A through P meets the opposite side BC at D....

Extracted text: The barycentric coordinates of a point P with respect to the non-collinear points A, B,C is given by P = (a:ß:y)ABc, where a +B +y = 1. The cevian from A through P meets the opposite side BC at D. Prove that the barycentric coordinates of P with respect to the points A, D is given by P = (a : ß +y)aD- In AABC, poins D, E are on the sides BC,CA such that BD: DC = 1 : 2, CE: EA = 2 : 3. The cevians AD, BE meet at P. Find the barycentric coordinate of P with respect to ABC. (Hint: Assume P= aA+BB +yC, with a + B +y = 1. Apply part a) to D andE to find a, B,y. )