1. Given two distinct points A and B in the plane, find all points C so that triangle ABC is isosceles.

(Note, a triangle is said to be "isosceles" when at least two of its sides have equal lengths. Or to put it another way, a triangle is isosceles when not all of the side lengths are different.)

The next one is a little more mathy:

2. Given two distinct points A and B in the plane, find all points C so that triangle ABC is a right triangle.

It makes a nice image if you carefully draw the answers to (1) and (2) on the same sheet of paper.

3. What would be the answers to (1) and (2) if the two points A and B were given in three-dimensional space, instead of a plane?

I'm using a new laptop that doesn't have any drawing software on it, so I'll have to post the answers later. Or, feel free to upload your answer to the Web someplace and link to it in the comments!

## 2 comments:

I put my drawing up here on my new blog. The blue marks are for the isoceles triangles and the red marks are for the right triangles. A fun trio of puzzles!

Nice Reid! Looks right to me. For fun you might prove your answer correct in the right triangle case...

I've been wondering what it would look like if the condition on triangle ABC is that it has a 20-degree angle. :-)

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