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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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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