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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

The challenge here is to visualise the diagram.

You can reason that a symmetrical solution is likely and then concentrate on the shape that is enclosed by the line segments. Calculate the angles and lengths in this shape before calculating the required lengths of the line segments.

You will need some trigonometry. Don't get put off by the calculation. The solution only requires simple geometry of right-angled triangles and polygons.