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Show that the triangle of maximum area t...

Show that the triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.

Text Solution

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OB=9
BD=`sqrt(a^2-x^2)`
CD=`sqrt(a^2-x^2)`
AD=a+x<*(a+x)br> Area=`1/2*(a+x)*2sqrt(a^2-x^2`
A=`(a+x)sqrt(a^2-x^2`
`(dA)/(dx)=sqrt(a^2-x^2)+(a+x)/(2sqrt(a^2-x^2)`-2x=0.
`=2a^2-2x^2-2ax-2x^2=0`
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