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Show that of all right triangles inscribed in a circle, the triangle with maximum perimeter is isosceles.

Show that of all right triangles inscribed in a circle, the triangle with maximum perimeter is isosceles.

Grade:12

1 Answers

saiomkar kandukuri
33 Points
8 years ago

a right angled triangle is possible in a circle if the hypotenuse is the diameter of the circle

the perimeter is x +y+ d

write y in terms of diameter and x....by using pythagorans theorem

then differentiate and equate to zero ...

you would get the value of x in terms of d

now find the value of y using the found x and d....by pythagoran theorem...

then u will find that y and x are equal....

this is the answer

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