Q: A large circle has a radius of 10cm Given four congruent circles tangent to one another within the large circle what is the radius of the largest circle which will fit in the middle?

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If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.

... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.

You join the centres of the two circles. Divide this line in the ratio of the two radii. Draw the tangent from this point to either circle and extend it to touch the other circle.

be equidistant from the center of the circle. APEX!

A straight line touches the circumference of a circle only at one point and it is a tangent line

Related questions

Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.

Yes.

No, tangent circles do not have the same center. They just touch at the side. Here is an example:

If the two circles are tangent to each other,then it must be at the same point.

If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.

No; tangent circles touch each other at one point but concentric circles cannot not touch.

Yes, circles that share one and only one point are tangent to each other.

Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.

Tangent circles.

... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.

An external tangent is a line that is tangent to both circles but does not pass between them.

They are the common tangents to the circles.