# Lines through triangle

• Dec 16th 2013, 05:07 AM
Encircled
Lines through triangle
Attachment 29922

http://i44.tinypic.com/1ivzb.jpg

See image A above
The black triangle is an isosceles triangle.
Consider the lengths of the parts of green and red line which are inside of the black triangle.
If I move the green and red lines together up or down, along the midaxis of the symmetric triangle,
do their relative lengths change?
(as long as they both remain inside of the triangle's top right and bottom corner)

Thanx beforehand!
• Dec 16th 2013, 06:57 AM
emakarov
Re: Lines through triangle
Quote:

Originally Posted by Encircled
If I move the green and red lines together up or down, along the midaxis of the symmetric triangle,
do their relative lengths change?

Yes, they do. When the red line is very close to the bottom vertex of the triangle, the ratio of green to red segments is arbitrarily large. When the green line passes through the top right vertex, the ratio is close to 1.
• Dec 16th 2013, 09:22 AM
Encircled
Re: Lines through triangle
Yes, how obvious it is with an example at the extreme.Thank you!