[surajms]

Yes. So, here when we rotate the triangle, we are essentially rotating each of the endpoints. For each endpoint, we rotate it by 180 degrees around the line segment joining the endpoint and the center. This by definition will result in a new position for each endpoint that creates a chord (as the two endpoints lie on the circle) and passes through the center (we rotated around it). A chord that passes through the center is by definition a diameter.

[HarHarVeryFunny]

Thanks. Thinking about it, another way of looking at it is to construct the rotated triangle by drawing a line from each point through the center to where it intersects with the circle on the other side. This is obviously a 180' rotation, but by construction we explicitly know the diagonal goes through the center.