# Answer to Riddle #87: Find the Length of the Line

87. Examine the diagram carefully. It shows a quadrant of a circle radius 'r', with a rectangle touching the perimeter of the circle. What is the length of the line labeled A-C.

Less of a Puzzle this than it is a trick, or at least when you see the answer in the form of another diagram with an extra line drawn on it you'll kick yourself:

Before reading the answer can I interest you in a clue?

This is one of those instances where it's easiest to show you the answer...

Is there another line in the diagram that is provably the same length as AC?

How about we draw that line in? Is there another name for this line? I know it seems like I'm slow walking you to nowhere but there is a reason... I'm very aware that by showing you the next diagram it will be obvious and I want that diagram to be below the fold.

If it's not clear from the diagram the extra line that is the same length as AC is a radius.

This is one of those instances where it's easiest to show you the answer...

Is there another line in the diagram that is provably the same length as AC?

How about we draw that line in? Is there another name for this line? I know it seems like I'm slow walking you to nowhere but there is a reason... I'm very aware that by showing you the next diagram it will be obvious and I want that diagram to be below the fold.

If it's not clear from the diagram the extra line that is the same length as AC is a radius.

**The length of AC is r.**© Nigel Coldwell 2004 - – The

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