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Arc Radius

Age 14 to 16 Short Challenge Level:

Triangle ABC is right-angled at A and side AB is 6 cm long.
An arc of radius $r$ cm is drawn with centre C such that it bisects side AC.
An arc of radius 6 cm is drawn with centre B such that the arcs both meet BC at the same point, as shown below.


   

Find the value of $r$.


This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.