What is inscribed and circumscribed in geometry?

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Inscribed Polygons and Circumscribed Polygons
Hi welcome to MooMooMath. Today we are looking at inscribed angles and what inscribed means and what circumscribed means when talking about polygons and circles. First we have a triangle and it is going to be inscribed in the circle. So I will draw the circle around the triangle so we say the triangle is inscribed in the circle. Now what if the circle is inscribed in the polygon? That just means it will be on the inside. So let me draw a polygon. I have a quadrilateral around the circle so we say we have a circle inscribed in the polygon. In order to be inscribed all the vertices need to touch the circle and the circle has to be tangent to the polygon. These are points of tangents so they touch in one point. Now let's look at circumscribed. If this polygon is circumscribed about the circle that means the circle is inside of it so we say the polygon is circumscribed about the circle. If the circle is circumscribed about the polygon polygon inside the circle, it can be any sized polygon in this case I have a hexagon inside it) So I would say the circle is circumscribed about the polygon. So that is the difference between inscribed and circumscribed. So a polygon inscribed in a circle means the polygon is inside. A circle that is inscribed in the polygon is on the inside

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