In ABC, seg BD bisects ABC. If AB = x, BC = x+5, AD = x-2, DC = x+2, then find the value of x.


Given BD bisects ABC.
Also AB = x, BC = x+5
AD = x-2, DC = x+2
Since BD bisects ABC, AB/BC = AD/DC [Angle bisector theorem]
x/(x+5) = (x-2)/(x+2)
Cross multiplying, we get
x(x+2) = (x+5)(x-2)
x2+2x = x2+5x-2x-10
x2+2x = x2+3x-10
x = 10
the value of x is 10 .

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