The problem is not difficult, tell yourself how to solve it!
First, write the equations of AC, AB, BP and CP, and calculate the coordinates of the intersection E of AC and BP. Similarly, calculate the coordinates of f, and point O is (0,0). Through two points, we can get the equations of OE and of.
See if you typed the question wrong again.
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AP:y =(-a/c)x+a； AB:y =(-a/b)x+a；
BP:y =(-p/b)x+p； CP:y =(-p/c)x+p；
Coordinates of point e
(-a/c)x+a =(-p/b)x+p x(E)= BC(p-a)/(CP-ab)；
Bring X into Y (E) = AP (C-B)/(CP-AB);
OE:y =(AP/BC)(c-b)/(p-a)x； simplify
( 1/b- 1/c)x+( 1/p- 1/a)y = 0
Similarly, x (f) = BC (P-A)/(Pb-AC);
y(F)= AP(b-c)/(p B- AC)；
OF:y =(AP/BC)(b-c)/(p-a)x； Simplified
( 1/b- 1/c)x-( 1/p- 1/a)y = 0。
From this problem, we can see that k(OE)=-k(OF).
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Off-topic: Math problems must be studied by yourself. You will make progress, and the sense of accomplishment after you make it is something you can't feel now.