The figure depicts OR as the perpendicular bisector of CR, forming right angles. OS is perpendicular to AC, making O the incenter. This determines OC as the angular bisector, yielding angle ROC as 62 degrees.
The figure displays a scenario where OR acts as the perpendicular bisector of CR, establishing a right angle at C (angle CRO = 90 degrees). Given that OS is perpendicular to AC, point O emerges as the incenter of triangle ABC. Consequently, OC becomes the angular bisector of angle ACB. The angles ACO and OCB both measure 28 degrees.
Now, to determine angle ROC, subtract the angles OCR and ORC from 180 degrees. The calculation yields 62 degrees (180 - 28 - 90). Therefore, angle ROC equals 62 degrees.
In summary, the figure illustrates the perpendicular bisector properties of OR and OS, leading to O being the incenter. This establishes OC as the angular bisector, resulting in angle ROC measuring 62 degrees.