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The in radius would be  \(a\sqrt3/6\)

Lets begin with the problem by find the slope of line b.

We know that if a line is perpendicular to another line the its slope hase an opposite sine (+ turns to -), and its the recipricol of it.

So, based of this piece of knowledge we know that the slope of line c is \(-2\), so the slope of line b is \(1/2\).

With this piece of info we can easily find the slope of line a!

Parallel lines have equal slope so now we know the slope of line a is \(1/2\) as well!! 

Now lets find the equation of line a using point-slope form!

Point-Slope Form: y=m(x-x₁)+y₁

We know it goes through the point \((1,2)\) so we can use this as our point, and we can use \(1/2\) as our slope!
Now we have the equation of line a!:

\(y=1/2(x-1) +2\)

\(y=1/2x+3/2\)

Great! But, this isn't our answer, but... we can use this equation to find our answer!! 
To find the y-intercept of a certain line, we must replace x with \(0 \)! That's super easy!

\(y = 1/2(0)+3/2\)
\(y = 3/2\)

So our answer is \((0,3/2)\)!!! 

Hope this helped!

Other users, if you see a mistake please reply with your answer! I make mistakes!!

As you can see in the sqaure roots we can extract the x^2's, as \sqrt{x^2} = x, we can do the same with the 4 and our equation(s) become:

2x + x = 6 + 3x  (1)

-2x + x = 6 + 3x  (2)

2x - x = 6 + 3x  (3)

-2x - x = 6 + 3x  (4)

!! Notice the signs as (-2)^2 = (2)^2, and the prblem is asking us to find all values of x !!

Solving the equations we get that x=:

(1): x = no solution

(2): x = -3/2

(3): x = -3

(4): x = -1

So our answer is -3, -1, and -3/2! 

Hope this helped!

Other user, if you see a mistake please reply with your answer! I make mistakes!!