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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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Pericut

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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Kissing

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?

Spokes

Stage: 5 Challenge Level: Challenge Level:1

circle and 3 sticks Draw three equal line segments in a unit circle so that they divide the disc into four parts of equal area.

What length do the line segments have to be?

Generalise this result.