Two circles having radius a cm and b cm touch each other externally. Another circle whose radius is c cm touches both the circles and also their common tangent. Which statement will be true?

For two circles of radii a and b touching externally, and a third circle of radius c touching both circles and their common tangent (inscribed in the curvilinear triangle), the relationship is 1/√c = 1/√a + 1/√b. Rearranging: √c = √ab/(√a + √b). Cross-multiplying and manipulating gives √bc + √ac = √ab, which is option D. This is a known result for circles tangent to two given circles and their common external tangent.