Question

The incentre of the triangle formed by the line `3x + 4y-12 = 0` with the coordinate axis is
A. (1/2,1/2)
B. (1/1)
C. (1,1/2)
D. (1/2,1)

Answer 1

Correct Answer - B

Answer 2

Incenter of a Triangle formed by coordinate axes in first quadrant is ( r, r ) where r is the radius of the incircle.

distance of ( r, r) from third side 3x + 4y - 12 = 0 will be radius r

r =  modulus (  [ 3r + 4r -12] / sqrt( 3² + 4²) )

r =  modulus (  [ 7r -12] / 5 )

case 1

r = - (  [ 7r -12] / 5 )

5r = -7r + 12

r = 1

case 2

r =  (  [ 7r -12] / 5 )

5r  = 7r - 12

r = 6

r = 6 is a big circle will not satisfy the conditions

so r = 1 is right answer