Posted by Stranger on .
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 
Steve,
Hmm. Place point D such that ABCD is a rectangle.
Let the center of the semicircle be at point O on AC.
Draw another semicircle 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 
student,
its wrong steve

Maths 
Kishan,
199