Proof that M is the Incenter.

Expression 23: "F" Subscript, 1 , Baseline equals "C" Subscript, 1 , Baseline plus StartFraction, "C" Subscript, "F" , Baseline Over "B" Subscript, "C" , Baseline , EndFraction left parenthesis, "B" Subscript, 1 , Baseline minus "C" Subscript, 1 , Baseline , right parenthesis

equals

17.9 9 1 3 0 7 5 7 8 7

Expression 24: "F" Subscript, 2 , Baseline equals StartFraction, "C" Subscript, "F" , Baseline Over "B" Subscript, "C" , Baseline , EndFraction "B" Subscript, 2 , Baseline

equals

6.5 1 9 3 1 5 9 4 4 3 7

Expression 25: "L" Subscript, 1 , Baseline equals "M" Subscript, 1 , Baseline

equals

13.2 0 7 6 8 7 3 8 4 7

Expression 26: "L" Subscript, 2 , Baseline equals "A" Subscript, 2 , Baseline equals 0

equals

Expression 27: "m" Subscript, 1 , Baseline equals StartFraction, "E" Subscript, 2 , Baseline Over "E" Subscript, 1 , Baseline minus "C" Subscript, 1 , Baseline , EndFraction

equals

negative 0.9 9 8 6 6 7 5 5 5 5 5 5

Expression 28: "m" Subscript, 2 , Baseline equals StartFraction, "F" Subscript, 2 , Baseline Over "F" Subscript, 1 , Baseline , EndFraction

equals

0.3 6 2 3 5 9 2 0 6 8 4 7

Expression 29: "m" Subscript, 1 , Baseline left parenthesis, "x" minus "C" Subscript, 1 , Baseline , right parenthesis equals "m" Subscript, 2 , Baseline "x"

Expression 30: "M" Subscript, 1 , Baseline equals StartFraction, "m" Subscript, 1 , Baseline "C" Subscript, 1 , Baseline Over "m" Subscript, 1 , Baseline minus "m" Subscript, 2 , Baseline , EndFraction

equals

13.2 0 7 6 8 7 3 8 4 7

Expression 31: "M" Subscript, 2 , Baseline equals "m" Subscript, 2 , Baseline "M" Subscript, 1 , Baseline

equals

4.7 8 5 9 2 7 1 2 4 9 9

Graphs

Expression 33: "y" less than 40

Hidden Label: "E" , "M"

Label

equals

left parenthesis, 9.8 0 7 , 8.1 8 2 , right parenthesis

left parenthesis, 13.2 1 , 4.7 8 6 , right parenthesis

Hidden Label: "F" , "M"

Label

equals

left parenthesis, 17.9 9 , 6.5 1 9 , right parenthesis

left parenthesis, 13.2 1 , 4.7 8 6 , right parenthesis

Expression 36: left parenthesis, "M" Subscript, 1 , Baseline , "M" Subscript, 2 , Baseline minus "t" "R" , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum:

Expression 37: polygon left parenthesis, "B" , "D" , right parenthesis

Expression 38: polygon left parenthesis, "A" , "B" , "C" , right parenthesis

Expression 39: polygon left parenthesis, "A" , "M" , "C" , "M" , right parenthesis

Expression 40: left parenthesis, "M" Subscript, 1 , Baseline plus "R" cos "t" , "M" Subscript, 2 , Baseline plus "R" sin "t" , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum: 360

Expression 41: left parenthesis, "L" Subscript, 1 , Baseline plus cos 45 , "L" Subscript, 2 , Baseline plus "t" sin 45 left brace, "D" Subscript, 1 , Baseline less than or equal to "M" Subscript, 1 , Baseline , right brace , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum:

Expression 42: left parenthesis, "L" Subscript, 1 , Baseline plus "t" cos 45 , "L" Subscript, 2 , Baseline plus sin 45 left brace, "D" Subscript, 1 , Baseline less than or equal to "M" Subscript, 1 , Baseline , right brace , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum:

Expression 43: left parenthesis, "L" Subscript, 1 , Baseline plus cos 135 , "L" Subscript, 2 , Baseline plus "t" sin 135 left brace, "D" Subscript, 1 , Baseline greater than "M" Subscript, 1 , Baseline , right brace , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum:

Expression 44: left parenthesis, "L" Subscript, 1 , Baseline plus "t" cos 135 , "L" Subscript, 2 , Baseline plus sin 135 left brace, "D" Subscript, 1 , Baseline greater than "M" Subscript, 1 , Baseline , right brace , right parenthesis

domain t Minimum:

less than or equal to "t" less than or equal to

domain t Maximum:

Points