Angle inscribed in a semicircle
SAT glossary · Course Foundations
Definition
A semicircle is a 180^circ arc, so any angle inscribed in it is 90^circ. Whenever a triangle has the diameter as one side and its third vertex on the circle, it is right — the single most useful circle fact on the test, because it converts a circle problem into a Pythagoras problem.
Angle inscribed in a semicircle in plain English
Picture a circle cut exactly in half by a straight line through its center — that half-circle boundary is called a semicircle, and it always measures 180° around its curve. Now imagine any triangle where one full side of the triangle is that straight diameter line, and the third corner just touches somewhere on the curved edge. No matter where that third point sits on the arc, the angle at that corner will always be exactly 90° — a perfect right angle. This is a huge shortcut on the test: the moment you spot a triangle with a diameter as one of its sides, you instantly know it has a right angle, which means you can immediately use the Pythagorean theorem (a^2+b^2=c^2) instead of wrestling with harder circle formulas.
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