for help

[shun]

In triangle ABC, if the length of the base AB is 6, and the height on the AB side h = 3, what is the value range of AC / BC?



When I draw with GGB I found that when the circle of three points A, B, C was passed, and the center of the circle was on the line y = 3, the ratio was the largest or smallest. But I still do n’t know why .

 

[Dr.Peterson]

What sort of answer are you looking for? "Why" can have different kinds of answer!

Have you tried proving it? Have you tried generalizing to cases where h is not half the base?

I did some experimenting of my own, and it looks like you're right; I haven't yet tried proving it, so I don't know if there is a simple proof that would make a "reason" apparent, but it's possible.

I'd probably try looking at theorems relating chords in a circle.

 

[shun]

What sort of answer are you looking for? "Why" can have different kinds of answer!

Have you tried proving it? Have you tried generalizing to cases where h is not half the base?

I did some experimenting of my own, and it looks like you're right; I haven't yet tried proving it, so I don't know if there is a simple proof that would make a "reason" apparent, but it's possible.

I'd probably try looking at theorems relating chords in a circle.