bisector of interior angle b and …
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Gaurav Seth 3 years, 11 months ago
Given:- ∆ABC is a triangle where BT and CT are internal and external bisectors of <ABC and <ACB respectively and they meet at T.
RTP:- <BTC = 1/2 <BAC
Construction:- Let, BC is produced to D and the external <ACD is formed.
Proof:-
In ∆ABC,
Exterior <ACD = interior opposite angle ( <ABC + <BAC )
=) 1/2 <ACD = 1/2 <ABC+ 1/2 <BAC
=) <TCD = <TBC + 1/2 <BAC ......( 1 )
In ∆TBC,
<TCD = <BTC + <TBC ........( 2 )
From ( 1 ) and ( 2 ),
<TBC + 1/2 <BAC = <BTC + <TBC
=) 1/2 <BAC = <BTC
=) <BTC = 1/2 <BAC
[ PROVED ]
1Thank You