AB is the diameter of a circle and C is any point on the circle. Show that the area of triangle ABC is maximum, when it is an isosceles triangle.
Let 'r' be the radius of the circle then,
Let BC = x units
we know that angle substracted by diametric in a circle in right angle
Then,
Now, area of
Differentaiating A w.r.t x , we get
The centrical number of x are given by
Now,
Again differentiating w.r.t x we get
Thus , A is maximum when
Putting in (i)
&
Hence A is maximum when the triangle is isosceles Hence proved