# Geometry Puzzle

• May 30th 2005, 11:04 AM
musamba
I really need a hint or a solution
Problem:
There is a point A with an angle. Let there be a point P in the angle. Make a line from B to C through P to give the triangle ABC minimum area.
[HTML]
/C
/
/
/ * P
/
A -------------B

• May 30th 2005, 11:26 AM
MathGuru
The area ABC seems to be predetermined.
Why does it matter where P is placed? there is only one possible line that goes through C and B.

• May 30th 2005, 12:30 PM
musamba
It doesn't matter where point P is placed. The difficult part about the problem is to draw a line to make the area smallest.
• May 30th 2005, 01:36 PM
MathGuru
But are point C and B already determined? If you can't move them there is only one possible line you can draw between them. I think I am missing something here.

Remember a line is the shortest possible distance between two points so unless we can move the two points in the line we can't really minimize the area.

Maybe if you give me some background for the question. Is this for school or is it for something else. What have you been studying recently that this question might be testing?
• May 31st 2005, 11:51 AM
musamba
No, that is exactly it. Point C and B are not determined.
The question is a geometry puzzle i came over, but i never found the solution and it is really stealing my sleep.
The question is not qurriculum based. The puzzles i came over can be solved by high school math.
I'm in my last year before starting of in college in autumn.
• May 31st 2005, 12:11 PM
Math Help
Okay
Why not make the angle between AB and AC very very small, even infinitaley small. Are there any other constraints to the problem?

Have you reproduced the problem in its entirety here?
• Jun 3rd 2005, 04:04 AM
hpe
Quote:

Originally Posted by musamba
No, that is exactly it. Point C and B are not determined.
The question is a geometry puzzle i came over, but i never found the solution and it is really stealing my sleep.
The question is not qurriculum based. The puzzles i came over can be solved by high school math.
I'm in my last year before starting of in college in autumn.

Make the triangle isosceles (i.e. B and C should have the same distance from A). There is a Calculus proof that this is minimal.