what is angle at baseline center point of an oblique triangle cut in half, from apex to baseline center?

Question

For an oblique triangle with points LTR where L is lower left, T top (apex), and R lower right:

Let C be the exact center point of baseline LR.

If imaginary line goes from point T down to point C, then what is angle TCR? The lengths of triangle's sides are known: LT LR TR The triangle's 3 angles at L, T, R can be derived using Law of Cosines.

But how to get angle TCR?

Answer 1

The law of cosines/ Stewart's theorem gives: $$ TC^2 = \frac{2\, TL^2+2\,TR^2-LR^2}{4} $$ hence you may find $\cos(\widehat{TCR})$ through the law of cosines, too.