Solution

Kitonum — Mon, 10 Dec 2012 19:32:57 Z

Use geometry package. Specify the coordinates of all the objects. The solution is obvious:

assume(y1>0, x2>0, x3>0, x3<x2):

point(A,0,0), point(B,x1,y1), point(C,x2,0), point(R,x3,0):

line(BC, [B, C]), line(AB, [A, B]), line(AC, [A, C]), ParallelLine(PR, R, BC):

intersection(P, PR, AB):

ParallelLine(PQ, P, AC):

intersection(Q, PQ, BC):

line(AQ, [A, Q]), line(BR, [B, R]):

intersection(M, PR, AQ), intersection(N, PQ, BR):

triangle(APM, [A, P, M]), triangle(PBN, [P, B, N]), triangle(RQC, [R, Q, C]):

S1, S2, S3:=area(APM), area(PBN), area(RQC);

is(S1+S2=S3);

MaplePrimes - answers and comments on Question, Geometry (Could you do more clearly?)