Angle chasing problem. (Euclidean Geometry solution preferred over analytic techniques)
Let $ABC$ be a triangle. Let $\angle ABC$ = 2B and let $\angle ACB$ = 2C $D$ is the foot of perpendicular from $A$ to $BC$. $I$ is the incentre of $ABC$. Compute $\angle BID$ in terms of B and C.
I was solving another question and this configuration came up. I have tried using basic angle chasing methods like looking for cyclic quadrilaterals after joining the incentre to all the vertices. Also tried dropping perpendiculars from incentre to the sides of the triangle. Please don't hesitate to try this too because I am very weak at geometry so I might have missed a property or two...
I think that this is an angle chasing problem for two reasons:
1)The original problem which I was solving gave me no other information about the triangle. The only thing I need is the expression for this angle using the angles of this triangle.
2)Also this angle, in my opinion gets fixed when we select the angles of the triangle...