(i) True. In an equilateral triangle, circumcenter and incenter coincide and hence both the circles can be drawn using the same center.
(ii) True, because while constructing an incircle, a perpendicular is dropped on a side and length of the perpendicular is taken as the radius.
(iii) False. Only in a right-angled triangle does the circumcenter lie on the hypotenuse.
(iv) True. The perpendicular bisectors of the sides intersect inside the triangle.
(v) False. Incenter is the intersection of the angle bisectors of two of the angles.
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