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Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Ford Circles

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We had two well constructed solutions from Katie of Firrhill High School and Zhi of St. Marylebone's School.
Here is Katie's solution.