Hi Ankit,
could you please specify the part in the solution you are having difficulty with?

A(Segment ABO2)= A(sector O2AO1B) - A(traingle O1AB) ??? I think this is not correct. It should be A(Segment ABO2) = A(sector O2AO1B) - A(sector ABO1)

Hi Ankit,
The solution has been modified for better understanding.
Hope this helps.

Hi Promel, we have improved the solution. Hope it is clearer now.

Hi Vishank,
Can you be little elaborate with your doubt?

it should be (2*pi)/3 instead of pi/3

Hi Vishank, Area of sector = (120/360)*pi*1^2 = pi/3 and not (2*pi)/3 as you are saying. If you are talking about doubling this area it has been done in the final step after subtracting the area of the triangle.

Hi Jaya,
Distance between O1 and O2 is 1 cm as this distance is equal to the radius of both triangles. Also O1A = O2A. Thus, the triangle O1O2A will be isoceles. So, O1P will bisect O1O2.

Hi Rekha,
Radius of both the circles is 1 unit. If you draw a perpendicular from O1 onto AB, it will bisect AB. Let the point where it intersects AB be M.
Then O1AM = 30°
Hence AM = O1A cos30 = 1cos30
=> AB = 2*1*cos30°
Hope this helps.

If you have any other query, feel free to ask.

Hello, we have added a diagram at the start to make the solution easier to understand. In the solution,

O1P = Half of O1O2 = 1/2 cm
So, the angle AO1P = 60 degrees as cos 60 = 1/2
By symmetry, BO1P = 60 degrees.
So, angle AO1B= 120 degrees

Hi, from the first figure, base =b=AB=2AP=2*OA1cos30 = 2*1cos30.

Hi, both circles are equal and their radii are 1cm. In triangle $$AO_1O_2$$, $$AO_1$$ is the radius. A$$AO_2$$ is the radius and $$O_1O_2$$ is also radius. So, all three sides are equal. Hence each angle is 60. So angle $$AO_1P\ =\ 60$$. Hope this answers your query.

Will add this to the pipeline and make a video as soon as possible

ok ty

Hi, can you please make a video solution?

Hi Ak,
I believe the mistake was while calculating the area of triangle CAD,
The height must be $$\frac{\sqrt{\ 3}}{2}$$ instead of $$\sqrt{\ 3}$$
Hope this helps

Hi GS,
We know that the chord AB is a chord to both the circles, and we also know that the line from the centre of the circle to the midpoint of the chord AB is also perpendicular to the chord. In this case, from symmetry, we can say that the line from the centre of the circles intersects AB at the midpoint of AB, and we know that the line is also perpendicular to AB. Hence, the angle $$APO_1$$ is 90 degrees.
hope this helps!