Semi-circle is all set to blow your mind !

Geometry Level 2

Given a right triangle \( \Delta ABC \) ; right angled at B .

If the measure of \( AB \) , \( BC \) and \( CA \) are \( 3 \) , \( 4 \) and \( 5 \) units respectively .

If the radius i.e \( \overline{OB} \) of the circle with centre \( O \) as shown , can be represented as \( \dfrac{a}{b} \) , where \( a \) and \( b \) are coprime .

Find \( a + b \).

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