Because the circle sits at eye-level, and also has the 40° line grazing its upper surface, then a line at 20° (half of 40°) would go thru the circles center.

This makes a triangle ABC with A being the eye, B being the base of the circle and C being the center of the circle. We know the circle has an angle at A of 20°, and line BC is 3m (half of the 6m diameter).

Solving this triangle: tan 20° = 3m / line length (AB), so AB = 3m / tan 20° = 8.24 m

The question asks "the distance the boy is from the nearest point of the tower.", well we have just figured out that the boy is 8.24m from the centre line of the tower, the tower is 6m in diameter, so he is 8.24 - 3 = 5.24m away from the outer wall

Now all that is left is that spike !