# A more direct way to see that the angle inscribed in a semicircle is $90^\circ$?

Like this inscribed angle proof, another proof enabled by this clever angle sum proof.

Is there a simpler way to show this?

Is this proof original?

• What is your question here? – B. Mehta Apr 15 at 3:16
• Sorry, "is it original?" (question edited) – hyperpallium Apr 15 at 3:24
• Very unlikely to be original. But I do like it. – fleablood Apr 15 at 4:18

Although this requires extending a line segment, I think it's easier to see that a $180^\circ$ line is divided in two (without algebraic rearrangment) - and the inscribed $90^\circ$ angle is right there, half of the line.