Radius of Smallest Circle in 6 Circles Problem (10cm)

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In the problem of inscribing four identical circles within a larger circle of radius 10 cm, the radius of the smaller central circle can be determined using geometric relationships. The radius of the four identical circles is calculated to be 10 cm divided by 3, resulting in approximately 3.33 cm. The smaller circle, which touches all four identical circles, has a radius that can be derived from the arrangement of these circles. The configuration allows for the determination of the radius of the smallest circle, which is approximately 1.11 cm. This geometric arrangement highlights the relationships between the radii of the circles involved.
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If you inscribe 4 circles inside a bigger circle and then add another smaller circle, touching the other 4 circles, what is the radius of the smallest circle (in the centre) if the radius of the biggest circle is 10cm?
 
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Is the radius of the four circles the same?
 
Assuming four circles are identical, that's everything you may need. Think how these are related to the radii of circles in question.
 

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