3 circles and a triangle
Here we have three unit circles, each of which intersect the three vertices of a scalene triangle.
What is the sum of the lengths of the part of the circles that are within the triangle?
Provide your answer to 2 decimal places.
If you think there isn't enough information, submit -1 as your answer.
The answer is 6.28.
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1 solution
The sum of the angles of the triangle is 1 8 0 ∘ .
So, the sum of the red angles in the picture will be 3 6 0 ∘ since each will be twice as large as the corresponding black corner in the same circle since an inscribed angle in a circle is 2 1 of the intercepted arc.
Therefore, the sum of the three purple lengths inside the triangle will be:
2 π = 6 . 2 8 to 2 decimal places.