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Home » AB is a diameter of a circle and C is any point on the circle. Show that the area of Δ ABC is maximum, when it is isosceles.
AB is a diameter of a circle and C is any point on the circle. Show that the area of Δ ABC is maximum, when it is isosceles.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
AB is a diameter of a circle and C is any point on the circle. Show that the area of Δ ABC is maximum, when it is isosceles.

Let consider AB be the width and C is any point on the circle with range r.

    \[\angle ACB\text{ }=\text{ }90o\]

 [angle in the semi-circle is 90o]

Let

    \[AC\text{ }=\text{ }x\]

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 47

Squaring on both the sides, we get

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 48

Hence, the space of

    \[\Delta \text{ }ABC\]

is least when it is an isosceles triangle.

i

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