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I love puzzles where there seems to be too little information. I found this one on the Mind Your Decisions YouTube channel.


If the radius of the circle is 8 units, find x.

How can we solve this when we don't know where on the diameter point P lies? Well, the mere fact that we aren't told where but are still expected to solve the problem, supplies the extra information we need. The length x must be the same wherever P is.

Very well then, we can choose anywhere we like. So let's pick the centre of the circle.

Now the angle marked in the triangle is 60 degrees, by subtraction from 180, and the two sides adjacent are radii of the circle, so their length is 8 units. Because of the 60 angle the triangle must be equilateral, and so the length of its third side is also 8.

So the answer is x = 8 units.