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**sydbernard****Member**- Registered: 2017-09-04
- Posts: 6

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.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,371

hi sydbernard

(1) I think it's only one as well. If the altitudes are AD and BE and they meet at G, then DGB = 60 and GDB = 90 implies DBG = 30.

BEC = 90 and CBE = 30 implies BCE (BCA) = 60.

(2) Work in progress.

Later edit: I am unable to draw a diagram for this at all. Let D be where the bisectors cross.

A + B < 180 implies DAB + DBA < 90. Therefore ADB > 90

Do you have a diagram?

Other post: I'm working on a method involving ellipses and circles. If successful I'll post on that thread later. Later edit: Done in other thread.

Bob

*Last edited by bob bundy (2017-11-10 01:13:07)*

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