Question

the area of a circle inscribed in the triangle formed by the line with equation x+y=1 and the two coordinate axes can be written in the form pi(a+b(sqr.c)/d) compute the value of a+b+c+d

Answer 1

The radius r of an inscribed circle in a right triangle with short sides u,v and hypotenuse w is given by:
r=uv/(u+v+w)
In the given case, the x and y intercepts are 1, so u=v=1, and w=√2.
Area of circle
= πr²
= π(u²v²)/(u+v+√2)²
=π(1²1²)/(1+1+√2)²
=π/(2+√2)²
=π(2-√2)²/(2²-2)²
=π(6-4√2)/2^sup2;
=π(3-2√2)/2
=π(1.5-1*(√2)/2)

I will leave it to you to figure out a,b,c and d.