Using the Baudhāyana–Pythagoras Theorem, equal chords with equal radii give equal perpendicular distances from the centre. Hence, chords of equal length are always equidistant from the centre of the circle.
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In an isosceles triangle, the altitude from the vertex bisects the base. The perpendicular bisector of a chord passes through the centre of the circle. Therefore, the altitude passes through the centre.
The two sides joining the centre to the endpoints of the chord are radii of the same circle. Since all radii are equal, the triangle formed is an isosceles triangle.
Yes. Other congruent triangles can be constructed on the same circumcircle. They have the same shape and size as the given triangle but are positioned differently on the circle.
The circumcentre is always equally distant from all three vertices of a triangle. Therefore, OA, OB and OC are equal. Small differences may appear only because of minor drawing or measuring errors.