Given the side length of one equilateral triangle and 3 radii R1, R2, R3 which produce 3 sectors inside the triangle. Calculate the area of the triangle which is not covered by the sectors.
My idea is
We can see there can be three cases.
- any radius from R1, R2, R3 is greater than or equal to S for which the answer will be Zero
R1+R2<S and R2+R3<S and R3+R1<Sso the answer will be Area of ABC — Area of 3 sectors
- if one sector intersects with another...
For this case, I will check if every pair of circle intersects or not. For this let's denote P as the intersection point. and let's draw a line PT which is perpendicular to the line AB. so from triangle APT and the new sector with an angle
60-Thetaso I can get the dashed area from Previous sector Area — (new sector area + triangle APT). with same this approach, I can get the opposite dashed area too which is calculated twice in the addition of sectors area since they intersect. So I'll subtract it from the original sector area.
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