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A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

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Age 14 to 16 Challenge Level:

Square with a random point selected inside

Can you prove that the sum of the distances of any point inside a square from its sides is always equal?

Can you prove it to be true for a rectangle or a regular hexagon?
Does the hexagon need to be regular?

Can you show the same is the case for a regular pentagon?
Does the pentagon need to be regular?