I think your confusion lies in this statement:

"But I thought a right triangle inscribed in a circle had to have a diameter as one of its sides?"

Conceptualize just that that for a moment: imagine a circle with a line running the diameter. This means you have essentially cut the circle in half since the diameter has to run through the center of the circle.

Now, with one line running border-to-border through the circle, where does the right angle vertices go? Answer: it can't go anywhere since the two ends of your line are touching the edges of the circle. Any movement to try and create a right angle at either edge of the line will result in that perpendicular line running OUTSIDE of the circle.

Make sense?

fltingley wrote:I think your confusion lies in this statement:

"But I thought a right triangle inscribed in a circle had to have a diameter as one of its sides?"

Conceptualize just that that for a moment: imagine a circle with a line running the diameter. This means you have essentially cut the circle in half since the diameter has to run through the center of the circle.

Now, with one line running border-to-border through the circle, where does the right angle vertices go? Answer: it can't go anywhere since the two ends of your line are touching the edges of the circle. Any movement to try and create a right angle at either edge of the line will result in that perpendicular line running OUTSIDE of the circle.

Make sense?

Ok, I was thinking that the only right angle that could exist in a circle was one that had a diameter as one of its sides. But I guess other types of 90 degree angles can exist within a circle. Is this correct?