STEP II 2007 question 8 solution

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i) Line through points B and C.

ii) Line AP =

Line BC =

They intersect when

So the point of intersection is

So, as required,

iii) It is first necessary to find the position vectors of F and E.

F is at the point where AB and CP intersect.

Line AB =

Line CP =

Line segment AF =

Line segment FB =

Similarly, E is the point of intersection of the lines CA and PB.

Line CA =

Line PB =

Line segment EA =

Line segment CE =

So

As required.

Solution by Dystopia.