Solucion 1.1

O: Circuncentro ;  R: Circunradio ; r: Inradio 
OM, ON y OQ : Mediatrices ;  ON' = ha ; OQ' = hb ; OM' = hc
x = MR ; y = NS ; z = QT

• QUEREMOS HALLAR EL VALOR DE  x+y+z

• HALLEMOS x

    • <R'MO = <N'OC = <A ,  MO = OC = R
       => ∆R'MO = ∆N'OC -> MR' = ON' = ha
    • x = MR = MR'+R'R ;  R'R = OQ' = hb
       => x = ha+hb  ...... [1]

• HALLEMOS y

    • <S'NO = <Q'OA = <B ,  NO = OA = R
       => ∆S'NO = ∆Q'OA -> NS' = OQ' = hb
    • y = NS = NS'+S'S ;  S'S = OM' = hc
       => y = hb+hc  ...... [2]

• HALLEMOS z

    • <T'QO = <M'OB = <C ,  QO = OB = R
       => ∆T'QO = ∆M'OB -> QT' = OM' = hc
    • z = QT = QT'+T'T ;  T'T = ON' = ha
       => z = hc+ha  ...... [3]

• Sumando [1], [2] y [3]:

    • x+y+z = 2(ha+hb+hc)
    • Usando Propiedad 1.4 : x+y+z = 2(R+r) = 2(6+2)
    • => x+y+z = 16 m.

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