# Math

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Let AB be the diameter of circle Γ1. In the interior of Γ1, there are circles Γ2 and Γ3 that are tangent to Γ1 at A and B, respectively. Γ2 and Γ3 are also externally tangent at C. This exterior tangent cuts Γ1 at P and Q, with PQ=20. The area that is within Γ1 but not in Γ2 or Γ3 is equal to Mπ. Determine M.

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10

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wrong

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should be 26

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WRONG!!!

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wrong dr.cao.....

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wrong de.cao

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wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....
wrong dr.cao.....

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calm down dr.cao 3rd
calm down

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50
Let the radius of larger circle be a, smaller ones be 'b' and 'c'.
Ans = pie(a^2-(b^2+c^2)) here we are only concerned with (a^2-(b^2+c^2))=
(a^2 - ((b + c)^2 - 2bc) = 2bc as a=b+c
Using intersecting chord theorem,
2bc= AC*BC/4= PC*CQ/4= 10*10/4 as diameter bisects chord
= 50 Ans

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SORRY GUYS I MEANT TO SAY ITS 60 SORRY DON'T USE 50 ITS 60!!