AP EAMCET202022 Sep 2020Evening ShiftMathematicsStraight LinesActual
The incentre of triangle formed by the lines x+y=1, x=1, y=1 is
Options
- A(1- 1 2 , 1- 1 2 )
- B(1- 1 2 , 1 2 )
- C( 1 2 , 1 2 )
- D( 1 2 +1, 1 2 +1 )
Correct answer
C. ( 1 2 , 1 2 )
Step-by-step solution
Given lines are, array rlrl & A & =(1,0) & B & =(0,1) P & =(1,1) & a & =B p=1 b & =A p=1 c & =A B= 2 array Incentre of, aligned P A B & = ( a x₁+b x₂+c x₃ a+b+c , a y₁+b y₂+c y₃ a+b+c ) & = ( 1(1)+1(0)+ 2 (1) 2+ 2 , 1(0)+1(1)+ 2 (1) 2+ 2 ) Incentre & = ( 1+ 2 2+ 2 , 1+ 2 2+ 2 ) aligned Consider, aligned 2 +1 2+ 2 & = 2 +1 2+ 2 2- 2 2- 2 = ( 2 +1)(2- 2 ) (2)^2-( 2 )^2 & = 2 2 -2+2- 2 4-2 = 2 2 1+ 2 2+ 2 & = 1 2 aligned Incentre becomes = ( 1 2 , 1 2 ) Hence, option (3) is correct.