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**sydbernard**- Replies: 1

1. Compute the angle at C of the triangle ABC if the altitudes at A and B intersect each other at an angle measuring 60◦. Consider all possibilities.

2. Compute the angle at C of the triangle ABC if the internal angle bisectors at A and B intersect each other at an angle measuring 60◦. Consider all possibilities.

So for 1 I think there is only 1 possibility in that the angle at C is 60 but are there actually more possibilities?

For 2 I think there are two possibilities depending on where the 60 is but I can't seem to figure out what the angle at C should be.

**sydbernard**- Replies: 2

Construct a triangle ABC given its side AB, the sum of the other two sides AC + CB and its angle at C.

**sydbernard**- Replies: 1

Construct a circle tangent to two given parallel lines and tangent from the outside to a disk lying between them.

I know that I need to construct a perpendicular between the 2 lines and bisect the segment which will then be the radius of the needed circle. But I thought I had to add the radii from the two circles together then from the center of the given disk make the desired circle but it's not working out.

**sydbernard**- Replies: 1

1. For which numbers n can it happen that a (not necessarily convex) pentagon has exactly n diagonals lying entirely in its interior? For each possible n, draw an example of a pentagon with exactly that many such “internal diagonals”.

2. Can a convex broken line self-intersect? (If yes, give an example, if no, give a proof.)

Thank you!

**sydbernard**- Replies: 4

Give an example that disproves the proposition “If the bisectors of two angles with a common vertex are perpendicular, then the angles are supplementary.” Is the converse proposition true? I've only been able to come up with examples that prove this proposition and can't think of any that show it's false.

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