We have received two good solutions to this problem.

Biren Patel (aged 14) from The Heathland School approached it like this:

The question asks you to prove that a+b=c.

You already know that the two lines are parallel.This tells us that they have the same gradient.

To work out the gradients we should try to imagine we draw a right angled triangle under both lines.

We then divide the change in the y-axis by the change in the x-axis.

The change in the x-axis of the line AB is equal to b-a (small letters refer to the co-ordinates).

We know that both lines, AB and OC are parallel, and so they must have the same gradient.

So b+a = c

Andrei Lazanu (aged 12) from School No. 205 in Bucharest (Romania), approached it in a slightly different way:

Let y = mx + n be the equation of the line going through the points A(a, a ²) and B(b, b ²).

The line OC passes through the origin and the point C(c, c ²).

Well done to you both.