8 August 2013

Puzzle: Radius of a circle

Returning from Salt Lake City. Today’s is a geometry puzzle.

In the picture below, the shaded rectangle is 4 cm by 2 cm. Can you find the radius of the circle?


Posted August 8, 2013 by Rajib Roy in category "Puzzles


  1. By Rajib Roy (Post author) on

    The answer is indeed 10. LEt me see if I can explain in words without drawing pictures. Draw two radius – one from center to the middle of the bottom side of the outer square. Draw another one from the center to the middle of the left side of the outer square. Now draw two more lines – extend the right side of the shaded rectangle upwards and the top side of the rectangle to the right. So, now you have a rectangle inside the circle (one corner of which is the center). Note that the rectangle sides are (r-2) and (r-4). Apply Pythagorus Theorem : (r) squared = (r-2) squared plus (r-4) squared. That will give you two answers – one os 10 and the other is impossible


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