The catheti AC and BC in a right-angled triangle ABC have lengths b and a, respectively. A circle centered at C is tangent to hypotenuse AB at point D. The tangents to the circle through points A and B intersect the circle at points E and F, respectively (where E and F are both different from D). Express the length of the segment EF in terms of a and b. Tangentscircleright trianglegeometry