Let $D$ be a point on side $BC$ of $\triangle ABC$. Let $K$ and $L$ be the circumcentres of $\triangle ABD$ and $\triangle ADC$, respectively.
Prove that $\triangle ABC$ and $\triangle AKL$ are similar.
Can I get a small hint on how to go start?
BL is a straight line and and ABDL is a kite. I think it can be proved by AAA. I've got that side AL is a diameter of circle AKL but don't know how to link it to angles A,B,C.