Logical circle

Geometry Level pending

If a circle touches both the axes ( $x$ -axis and $y$ -axis), and also it touches a circle $x^2+y^2=a^2$ in first quadrant, then what is the radius of the circle if $a=\sqrt2-1$ . b>a.

The answer is 1.

2 solutions

Akash Shukla
Mar 19, 2016

yes,Thanks . I have discovered my mistake . There is another circle inside the given circle which follow the given condition.so to have only one solution b<a or b>a

Andreas Wendler
Mar 19, 2016

A program solving non-linear equations' systems has input:

(m-r)/(s-n)=-r/s

b=n

(a-m)^2+n^2=u^2

m^2+(b-n)^2=u^2

-(m-a)/n=0

(r-m)^2+(s-n)^2=u^2

r^2+s^2=(sqrt(2)-1)^2

Here (m, n) is midpoint of searched circle and u its radius, (s, t) denotes the touch point between the two circles and a and b are the touch points with x- respective y-axis. The solution is:

r = 0,292893218813 s = 0,292893218813 m = 1 n = 1 b = 1 a = 1 u = 1

Unfortunately the solution is not unique. Another one where the circle we seek is located into the given one is this:

r = 0,292893218813 s = 0,292893218813 m = 0,171572875254 n = 0,171572875254 b = 0,171572875254 a = 0,171572875254 u = 0,171572875254

Logical circle

The answer is 1.

2 solutions

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