A geometry problem by Gilbert Calvo
Geometry
Level
pending
What the area of the biggest circle?
(note: all the lines are straight. I don't know the answer that's why I put zero)
The answer is 0.
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1 solution
ans. is 25π.
Label the centre of circles A(of the biggest circle),B(of the second largest circle) and C(the smallest circle).
The points of intersection as D(of biggest circle and smallest circle), E(of second largest circle and the smallest circle) and the remaining point F. AF=AD,CD=CE,BE=BF(Radius of same circles).............(1)
Now, AD+CD=8................(Equation 1) BE+EC=10..................(Equation 2) AF+BF=12....................(Equation 3) AD+BE=12....................(Equation 3) (From 1)
Subract Eq.3 from Eq.1 AD+CD-AD-BE=8-12 CD-BE=-4..................................(Equation 4)
Add Eq.2 and Eq.4 BE+EC+CD-BE=10-4 2CD=6.........................................(From 1) CD=3..............................(2)
Now, AD+CD=8 AD+3=8 AD=5...........(Radius of bigger circle)
Area=πR^2=5^2π=25π.................Ans.