



 
Hi Adrian, Since triangle ABC is a right triangle you can use Pythagoras theorem to find the length of CA. Since the vertices of the right triangle ABC are on a circle, CA is a diameter of the circle and hence R is half the length of CA. G is the centre of the small circle and D, E, and F are the points where the small circle is tangent to the sides of the triangle ABC.
The last of these pairs of congruent triangles tell us that angles EBG and GBF are congruent and hence each measures 45 degrees. Thus EB = BF = r. Can you complete the problem now?  


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