The two triangles have equal radii as corresponding sides and equal chord lengths as their bases. Therefore, all three corresponding sides are equal, so the triangles are congruent by the SSS Congruence Criterion.
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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.
No. There is no point that is equally distant from three collinear points. The perpendicular bisectors of AB and BC are parallel and never intersect. Therefore, no circle can pass through three collinear points.
The least possible radius is obtained when the two given points are the endpoints of the diameter of the circle. Therefore, the smallest radius equals half the distance between the two points.