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A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum area of the triangle, in square units?

 Aug 15, 2020
 #1
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The largest triangle, by area, that can be inscribed in a triangle is the equilateral triangle.  Since you need a right triangle, you can swing one of the points to the other, which gives you a 30-60-90 triangle, with sides 50, 50*sqrt(30), and 100.  The area of this triangle is 1/2*50*50*sqrt(3) = 1250*sqrt(3).

 Aug 15, 2020
 #2
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A right triangle is inscribed in a circle with a diameter 100 units long. What is the maximum area of the triangle, in square units?

 

The largest right-angled triangle inscribed in a circle is an isosceles right triangle.

 

area = 1002 / 4

 Aug 16, 2020
edited by Dragan  Aug 16, 2020

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