Arc radius

Two arcs are drawn in a right-angled triangle as shown. What is the length $r$?
Age
14 to 16
Challenge level
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Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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.

Arc Radius
   

Find the value of $r$.

This problem is adapted from the World Mathematics Championships