#Александър Чаушев
#16-Б / ИУ 7
import math

xA = float (input("Type in X coordinates first point: "))
yA = float (input("Type in Y coordinates first point: "))
xB = float (input("Type in X coordinates second point: "))
yB = float (input("Type in Y coordinates second point: "))
xC = float (input("Type in X coordinates third point: "))
yC = float (input("Type in Y coordinates third point: "))

AB = math.sqrt((xB-xA)**2 + (yB-yA)**2) #c
AC = math.sqrt((xC-xA)**2 + (yC-yA)**2) #a
BC = math.sqrt((xC-xB)**2 + (yC-yB)**2) #b
cosA = (BC**2+AB**2-AC**2)/2*BC*AB
cosB = (AC**2+AB**2-BC**2)/2*AC*AB
cosC = (AC**2+BC**2-AB**2)/2*AC*BC
p = (AB+AC+BC)/2
list1 = [cosA, cosB, cosC]


checkX = (xA - xC)/(xB - xC)
checkY = (yA - yC)/(yB - yC)

if checkX == checkY:
      print("This is not a triangle!")
else:
      print("AB: {:7g}".format(AB))
      print("AC: {:7g}".format(AC))
      print("BA: {:7g}".format(BC))

if max(list1) == cosA:
     Ha = (2/AC)*math.sqrt(p*(p-AC)*(p-BC)*(p-AB))
     print("Height: {:7g}".format(Ha))
if max(list1) == cosB:
     Hb = (2/BC)*math.sqrt(p*(p-AC)*(p-BC)*(p-AB))
     print("Height: {:7g}".format(Hb))
if max(list1) == cosC:
     Hc = (2/AB)*math.sqrt(p*(p-AC)*(p-BC)*(p-AB))
     print("Height: {:7g}".format(Hc))

if cosA < 0 and cosB > 0 and cosC > 0:
    print("triangle is Obtuse")
elif cosB < 0 and cosC > 0 and cosA > 0:
    print("triangle is Obtuse")
elif cosC < 0 and cosA > 0 and cosC > 0:
    print("triangle is Obtuse")
else:
    print("triangle is not Obtuse")

xN = float (input("Type in X coordinates first point: "))
yN = float (input("Type in Y coordinates first point: "))

sumA = xA + yA
sumB = xB + yB
sumC = xC + yC
sumN = xN + yN

SumA1 = sumA - sumN
SumB1 = sumB - sumN
SumC1 = sumC - sumN


if xA > xB and xA> xC:
    biggestX = xA
if xB > xA and xB > xC:
    biggestX = xB
if xC > xA and xC> xB:
    biggestX = xC

if yA > yB and yA > yC:
    smallestY = yA
if yB > yA and yB > yC:
    biggestY = yB
if yC > yB and yC> yA:
    biggestY = yC


if xA < xB and xA < xC:
    smallestX = xA
if xB < xA and xB < xC:
    smallestX = xB
if xC < xA and xC < xB:
    smallestX = xC

if yA < yB and yA < yC:
    smallestY = yA
if yB < yA and yB < yC:
    smallestY = yB
if yC < yB and yC < yA:
    smallestY = yC


if xN <= biggestX and xN >= smallestX and yN <= biggestY and yN >= smallestY:
    print("point N is in the Triangle")
else:
    print("point N is not in the Triangle")

if SumA1 > SumB1 and SumA1 > SumC1:
    distanceA1 = math.sqrt((xN-xA)**2 + (yN-yA)**2)
    print("Distance to the farest point is: {:7g}".format(distanceA1))
elif SumB1 > SumA1 and SumB1 > SumC1:
    distanceB1 = math.sqrt((xN-xB)**2 + (yN-yB)**2)
    print("Distance to the farest point is: {:7g}".format(distanceB1))
elif SumC1 > SumB1 and SumC1 > SumA1:
    distanceC1 = math.sqrt((xN-xC)**2 + (yN-yC)**2)
    print("Distance to the farest point is: {:7g}".format(distanceC1))