In a triangle abc ab = bc A point D is marked inside the triangle so that the angle dac = dca. Prove that the intersection point

In a triangle abc ab = bc A point D is marked inside the triangle so that the angle dac = dca. Prove that the intersection point of the heights of this triangle lies on the line bd.

BO – height => (T to isosceles triangle) => BO – mediatrix => O – middle. OD – mediatrix of triangle ADC triangle ADC – isosceles, with base AC => OD – height of triangle ADC => points B, O, D – collinear (On one straight line) => The point of intersection of heights of triangle ABC lies on straight line BD.