Please solve q 57 ?

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1 Answer
CW
May 11, 2018

#CD+CE=S/2#

Explanation:

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Let #O and r# be the center and the radius of the incircle, as shown in the figure.
Given #AB+BC+CA=S#
Let #|ABC|# denote area of #DeltaABC#,
#=> |ABC|=1/2*r*(AB+BC+CA)=1/2rS#
given #DE# divides #DeltaABC# into two equal areas,
#=> |CDE|=1/2|ABC|=1/4rS ----- Eq(1)#
#|CDE|=1/2*r*(CD+CE) ----- Eq(2)#
As #Eq(2)=Eq(1)#,
#=> 1/2*r*(CD+CE)=1/4rS#
#=> CD+CE=S/2#

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