Find the value of x for this shape with a circle inside it:

check the picture below.

as you know, two tangent lines to the same circle, when they meet, their length is the same, therefore, as you see in the picture, a = a, b = b, c = c, those tangents are three twins.

also recall that the point of tangency, where the radius touches the tangent line, is always a right-angle, as you see there.

and we know the lengths of a + c = 15, a + b = 12 and b + c = 9.

we can write them as a system of equations of 3 variables, and we'll do some elimination, so let's proceed.

which we can again write it as -a + b + 0c = -6.

and now, let's use that resultant equation and use it with the second equation as is

if you use photomath right away it will give you the answer not like this app that you have to wait for people.