Squares, triangles... and a circumference!
Geometry
Level
3
-
A square
is inscribed in a circumference.
- Find the AREA of the RED TRIANGLE, rounding it to the SECOND decimal figure.
- The measure of the length of the circumference is .
- is the center of the circumference.
The answer is 0.22.
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1 solution
From the circumference it's easily deducted that the radius of the circle is 2 2 2 . Making use of a 45-45-90 triangle this leads to the side lengths of the triangle, down left of the square. The lengths are 1 1 1 . So the are is 55.5. Now the red triangle has side 4 times as small(its halved 4 times), so the area is ( 1 6 1 ) 4 as small. So the area is 0.22