Question 125
Choose points $H,K,M$ on the sides of triangle $ABC$ so that $AH$ is an altitude, $BK$ an angle bisector, and $CM$ a median. Let $D=AH\cap BK$ and $E=HM\cap BK$. Given $KD=2,DE=1,EB=3$:
(i) Prove that $HM\parallel AC$;
(ii) Prove that $AB=AC$;
(iii) Prove that $AB=BC$.
(i) Prove that $HM\parallel AC$;
(ii) Prove that $AB=AC$;
(iii) Prove that $AB=BC$.