[Math] Is that possible that a inscribe angle can be greater than 90 degree

circlesgeometry

I have found a question like following:

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Its asked that what could be the angle $x$ if $BC$ is not diameter of the circle.

So, my question is if it possible to be greater then $90^{\circ}$ for an angle like $x$?

My proof said:

The highest inscribed angle only could be made of with the chord same diameter. The other chords could not create an angle greater than that.

Best Answer

Yes, the angle can get very close to (but not exactly equal to) 180 degrees. For every angle value greater than 90-degrees the chord $\overline{BC}$ is smaller than the diameter.

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