Q1.prove that maximum area of right triangle inscribed in a circle is isosceles

Asked by  | 6th Mar, 2009, 08:46: PM

Expert Answer:

Given a circle with radius r.

Let triangle ABC be a right triangle inscribed in the circle.

Since the triangle is a right triangle, hence one of the angle is 90o.

Let angle C = 90o

Then AB is diameter of the circle, since angle in semi circle is 90o

Hence, AB= 2r, let BC=x and AC = y

Area of traingle ABC = A = 1/2 * x*y

Applying pythagoras theorem in triangle ABC, we het

y = ((2r)2-x2) = (4r2-x2)

Putting this value of y in area

A = 1/2 * x * (4r2-x2)

Differentiating A with respect to x, we get

Answered by  | 20th Mar, 2009, 12:38: PM

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