A black hole by definition does not emit radiation. In fact, it captures everything that falls onto it. So how do you observe something that does not radiate?

It is true that a black hole itself does not emit light. However, the EHT observes the nearby surroundings of a black hole. The gas that surrounds the observational targets of the EHT does in fact radiate, so by observing this region the EHT may observe structures that result from the strong gravity of the black hole.

Are there more black holes, other than Sgr A*, in our Galaxy?

It is predicted that many smaller black holes of roughly stellar size exist throughout any galaxy. We study supermassive black holes Sgr A* and M87 because their apparent sizes are much larger than these stellar sized black holes when viewed from the Earth, so they are easier to study.

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