Our+PM2+project+findings

I just remembered: Add restrictions! Maybe we can work on the ratio of the triangles the the circles that have odd ratios...

Jia Wei, I have checked your answer for the question about the pattern of the ratio change in the area of the circle and the largest triangle in the circle and I have found it correct. I have also checked my own ratios and there was also no pattern. Maybe you could try more complicated patterns like odd radius, even radius, or maybe even use an even more complicated pattern.

How do I know that equilateral triangle is the biggest?

My findings is that, when the circles radius is 3 cm (diameter 6cm), the area of the triangle is 12.19, thus, the ratio is 1219 : 2826. The triangle's base is 5.3cm, while the height is 4.6cm. Other triangles, like scalene and isosceles, is not as big as the equilateral triangle. Some of the areas are 12.005, 11.89 etc. Then I thought, if triangle's base is 4.6cm, can the height of the triangle be 5.3cm? I investigated and found out that the height can only be 5 cm, so the area is 11.5, which is smaller than the equilateral triangle.

So, we can conclude that the equilateral triangle is the biggest triangle that can be drawn in a circle.

Hi, Jia Wei. My findings is that the **ratio changes if the circle becomes bigger** __although i may have counted wrongly__. Pls check my work (__**larger circle diameter 8.6 cm, smaller circle diameter 6 cm**__). My findings is also the same... ( Jia Wei) Please check out the Question page as I have another question...