Question

The radius of the smallest circle which touches the straight line 3x-y=6 at (1, -3) and also touches the line y=x is,
(A) 1
(B) 1.6
(C) 1.49
(D) 0.5​

Answer 1

Answer:

b. 1.6

Step-by-step explanation:

Theory:

since both lines are tangent to the same circle, so smallest possible circle must have the diameter between these lines.

Approach:

find the perpendicular line to 3x-y=6 at (1, -3) which will be x+3y+8=0.(using negative inverse slope)

intersection of this perpendicular line with y=x at (-2,-2)

distance between (-2,-2) and (1, -3) is √10 => 3.16--> 3.2(dia)

radius : 3.2/2 = 1.6