As shown in the figure, the triangle ABC is the inscribed triangle of circle O, I is the inner part of triangle ABC, the extension line of AI intersects BC at point E, and intersects circle O at point D Come on, now, now!

As shown in the figure, the triangle ABC is the inscribed triangle of circle O, I is the inner part of triangle ABC, the extension line of AI intersects BC at point E, and intersects circle O at point D Come on, now, now!

I have done this problem
The picture looks like this
.A
.I
B.E.C
.D
Is it to prove DB = CD?
prove:
∵ ad bisection ∠ bac
∴∠BAD=∠CAD
∫∫ BDC = ∫ CAD ∫ bad = ∫ BCD
∴∠BDC=∠BCD
∴CD=BD
We can also prove BD = id = CD by using the angle relation
I hope my answer is useful to you. Have a good time