1. As shown in the figure, BD is the bisector of ∠ABC, DE⊥AB is in E, ∠ C = 90, ab = 36, bc = 24, and S △ ABC = 150. Find the long diagram of DC:

2. As shown in the figure, AD is the center line of BC side in △ABC, and the extension line of CE‖AB across AD is in E. Proof: (1)AB=CE(2)2AD figure:

3. As shown in Figure 1, BD and CE are the bisectors of the external angle of △ABC, point A is AF⊥BD and AG⊥CE, and the vertical foot is F and G, respectively, connecting FG, extending AF and AG, and intersecting with the straight line BC, it is easy to get FG= 1/2(AB+BC+AC). (2)BD is the bisector of the inner angle of △ABC, and CE is the bisector of the outer angle of △ABC (Figure ③). What is the quantitative relationship between the three sides of line FG and △ABC in Figure ② and Figure ③? Please write your guess and give a proof diagram of one of the situations:

I found these. You can keep the rest for yourself.