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In triangle ABC is the external bisector of angle A meeting BC produced at E . If AB=10cm, Ac 6cm&BC 12cm find CE

Posted by Prachi Ghosh 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

According to question It is given that in {tex}\triangle {/tex}ABC, AE is the bisector of the {tex}\angle CAD{/tex}.

Also, BE = BC + CE = 12 + x

CE= x, AB = 10, AC = 6
Since, We know that, the external bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
{tex}\therefore \frac { B E } { C E } = \frac { A B } { A C }{/tex}
{tex}\Rightarrow \frac { 12 + x } { x } = \frac { 10 } { 6 }{/tex}
{tex}\Rightarrow{/tex} 6(12 + x) = 10x
{tex}\Rightarrow{/tex} 72 + 6x = 10x
{tex}\Rightarrow{/tex} 4x = 72
{tex}\Rightarrow x = \frac { 72 } { 4 }{/tex}
= 18 cm
{tex}\Rightarrow{/tex} CE = 18 cm

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