# Tiny Segmental Area

Discussion in 'Online Games & Puzzles' started by Thyagarajan, Oct 29, 2022.

1. ### ThyagarajanFinest Post Winner

Messages:
10,113
10,931
Trophy Points:
590
Gender:
Male

How do we get the area of of tiny white segment in red circle bounded by blue arc and red straight line.
The black dot coordinates are as shown in brackets in fig above.​

2. ### hrastroFinest Post Winner

Messages:
1,455
3,335
Trophy Points:
283
Gender:
Female
On the first look, I thought I have to integrate the area under curve - so calculus would be the only way... but on further thought, if we could consider that the two segments on either side of the y-axis (Line ABC) are equal, it is now a simple matter of understanding circles and trigonometry and co-ordinate plane.

So, I named the points A,B,C,D and angle x as shown below. We need to find the area of the green portion. The answer is explained below - we get answer as [pi/3 - sqrt(3)/2] units...
Please do let me know if there is anything wrong or if something needs more explanation
Keep smiling
HR

Thyagarajan likes this.
3. ### ThyagarajanFinest Post Winner

Messages:
10,113
10,931
Trophy Points:
590
Gender:
Male
Delighted. Full Marks.
Regards.

hrastro likes this.