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I canīt resolve the next problem:
An athletics track is to have a perimeter of 400 m and straights of 78.
Find the radius r of the circular 'bend'.
(The problem has the answer: 38.8 m)
I attached the image...
Can you please help...
When i thought i finally have the answer is incorrect...

The bend in the track is a semicircle at both ends.
When boht ends are thought of at once, this forms a circle.
This radius around a circle is 2*pi*r.

If we take 78 as the length of a side, and there are two sides, that gives 2*78 = 156 as the side length.  If we then take 400 - 156 = 244, that gives the length left for the ends.

To find the raidus, we know the length of the ends is both 2*pi*r and 244.
Solving 2*pi*r = 244 gives r = 122/pi.  That should give a radius of around 38.8 meters.

To make the track fairly close to exact 400 m in length,
this raidus should be measured as 38.33 meters.
That's 33 cm beyond 38 meters, and it would be really hard to get it down to the mm.


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Scott A Wilson


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