A company is designing a new logo in the shape of a letter “C”. The letter “C” is formed between two circles with centre O. The point A lies on the circumference of the inner circle with radius $r$ cm, where $r<10$. The point B lies on the circumference of the outer circle with radius 10 cm. The reflex angle $A\hat{O}B$ is 5.2 radians. The letter "C" is shown by the shaded area in the following diagram.