Day 5 Inscribed Polygons

If all of the vertices of a polygon lie on a circle, the polygon is inscribed in the circle and the circle is circumscribed about the polygon. The polygon is an inscribed polygon and the circle is a circumscribed circle.

We’ll now examine theorems about inscribed polygons.

1^ST Theorem:

If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is a right angle.

2^ND Theorem:

A quadrilateral can be inscribed in a circle if and

only if its opposite angles are supplementary.

Proof:

Go to Day 6