【数学】 Ceva's Theorem メネラウスの定理 チェバの定理 解説用の図

Let's try an example.

What is the ratio of  ?/? of the following triangle?

This is how to figure it out...

Let's go one step further.

Adjust the ratio so as for A and D to be the same number.

Then, it always happens to be the fact that A = D, B = E, C = F.

Now you get the 3 numbers!

This is how you use these 3 numbers.

For example, if the there numbers are 6, 4, and 3, …

You can also figure out the ratio of the area of the 3 small triangles inside.

Let's try a sample question.

What is the ratio?

Could you figure it out?

Solution

Finally, you get the ratio on the all sides.

Do some adjustment, and get the magical 3 numbers!

In this case, those numbers are 2, 3, 4.

With those 3 numbers, you can figure out all of the following ratios!!!