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matt grime said:As it stands there isn't a solution to this question. You need to provide more information. Proof: just draw the two circles whose radii are given. pick one point on each circle. draw in the normal lines at thos points. where they intersect is the centre of a larger circle tangential to these two. draw it. you are then claiming that the circle you can inscribe that is tangential to all three is uniquely determined which is not the case, I believe.
honestrosewater said:Looks can be deceiving... you cannot form the right triangles as I thought. I also misspoke, as O_A and I_BC lie on some line, of course, but this line is not tangent to circles B and C.
Still happy thoughts
Rachel
The formula for finding the radius of a tangent circle is r = (sqrt(2) * d) / 2, where d is the distance between the centers of the tangent circles.
The shaded circle in a problem with multiple tangent circles is usually the smallest circle, as it is the one that is tangent to all the other circles.
No, the shaded circle must have a smaller or equal radius to the other tangent circles in order for it to be tangent to all of them.
Yes, if you know the radii of the other tangent circles, you can use the Pythagorean theorem to solve for the radius of the shaded circle. The formula is r = sqrt((r1 + r2)^2 - (d/2)^2), where r1 and r2 are the radii of the other tangent circles and d is the distance between their centers.
If the shaded circle is not tangent to all of the other circles, then it is not considered a tangent circle problem and a different approach must be used to find its radius.