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In the triangle OAB, OA=a and OB=b. M is the midpoint of AB and N is...

In the triangle OAB, OA=a and OB=b. M is the midpoint of AB and N is the point on OB such that ON:NB = 1:4. OM meets AN at P.

(a) Find and expression for OP in terms of a and b

(b) Deduce that AP:PN = 5:1.

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