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ABC is a right angled triangle with ∠ABC=90∘ and side lengths AB=24 and BC=7. A semicircle is inscribed in ABC, such that the diameter is on AC and it is tangent to AB and BC. If the radius of the semicircle is an improper fraction of the form a/b, where a and b are positive, coprime integers, what is the value of a+b?

  • Maths -

    Hmm. Place point D such that ABCD is a rectangle.

    Let the center of the semi-circle be at point O on AC.

    Draw another semi-circle centered at O, to form a complete circle. Since it is tangent to AB, it is also tangent to DC.

    So, the diameter of the circle is 7, and the radius is 7/2, so a+b=9.

  • Maths -

    its wrong steve

  • Maths -

    199

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