In Fig. 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, find CE.
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In Fig. 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm.
CE = 18 cm.
Given,
AE is the bisector of the exterior ∠CAD meeting BC produced in E.
AB = 10 cm
AC = 6 cm
BC = 12 cm
As we know that, the external bisector of an angle of a triangle divides the opposite sides externally in the ratio of the sides containing the angle.
So, we have the ratio
AB/AC = BE/CE
from figure, we have,
10/6 = (12+x)/x
10x = 6(12+x)
10x = 72 + 6x
10x - 6x = 72
4x = 72
x = 72/4
x = 18
Therefore, CE = 18 cm
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