Solving Geometric Problem - Find \angle ATB

[danne89]

Hi! My problem sounds as following:
In the isoscele triangle \triangle ABC, \angle A = 48 degrees. Bisect the angle \angle A against \overline CB in point T. Determine the \angle ATB for the three possible solutions.

I've found two of them, but cannot find the last.

The first one is if you pick A as one of the conjugent angles and then you get \angle ATB = 108 degrees.

The second one you find if you select the top angle and then get \angle ATB = 90 degrees.

 

[BobG]

If you bissect the angle against CB at point T you now have two triangles.

If A is the 'top' angle (i.e. B and C are equal), then both of the new triangles are identical to each other - it doesn't matter which of the remaining angles is B and which is C.

If A is one of the side angles (equal to either B or C), then the two new triangles are not equal to each other. If B is equal to A, then ATB is equal to 108 degrees as you said. But how about if A is equal to C and B is the top angle?

 

[danne89]

Ohh, I see now. Thanks! I was being misslead by myself.