Maximum Area of Isosceles Triangle Inscribed in a Circle Calculus

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Thanks Mondal to ask how the property of isosceles triangle is used in this solution: It is important to note that the altitude is AD, height of the triangle. Point D is midpoint of base BC since the triangle is isosceles. That is why we took x + x as the base.
CORRECTION : A(12) = 0 not 24
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Just wow you perfectly explained every step way too good thank you so muchh

Rin-gdvg
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There is a wonderful formula to find the area of any n-sided normal polygon inscribed in a circle:

(1/2)nr²sin(2π/n)

n=number of polygon sides
r=radius

sylowlover
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FINALLY!! MANY THANKS TO YOU!! i have been struggling on this problem for days!!

alisakulik
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you. are. the. goat. probably wouldve got a 70 on my calc exam without you

lvl
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Without radius of circle given, can you prove the maximum area of triangle is equilatetal triangle?

edwinloquina
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sir,
at y=12 we get the area equals to

muhammedyasser
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(.5)(3 number of side )(12 radius)^2 sin(360/3 number side ) = 187.06

christiandaro
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Sir where are you apply property of isosceles triangle ??

shibommondalmath