Name Theorem Hypothesis Conclusion A polygon whose Opposite angles are Inscribed Polygons vertices lie on the circle. supplementary. Example: Find the value of x and y. Example: Find the value of x and y. Example: Can this quadrilateral be inscribed inside a circle? Name Definition Measure Picture When a triangle is inscribed in a circle, the The circumcenter is Circumcenter center is called the equidistant from the circumcenter (formed by vertices of the triangle. perpendicular bisectors). Circle enclosed in a Inscribed Circle polygon, where every Or NA side of the polygon is Circumscribed Triangle tangent to the circle When a circle is inscribed in a triangle, the center is The incenter is Incenter called the incenter equidistant from the (formed by angle of the triangle. bisectors).
Name Theorem Hypothesis Conclusion Inscribed Polygons A polygon whose vertices lie on the circle. Opposite angles are supplementary. Example: Find the value of x and y. Example: Find the value of x and y. Example: Can this quadrilateral be inscribed inside a circle? Name Definition Measure Picture Circumcenter When a triangle is inscribed in a circle, the center is called the circumcenter (formed by perpendicular bisectors). The circumcenter is equidistant from the vertices of the triangle. Inscribed Circle Or Circumscribed Triangle Circle enclosed in a polygon, where every side of the polygon is tangent to the circle NA Incenter When a circle is inscribed in a triangle, the center is called the incenter (formed by angle bisectors). The incenter is equidistant from the of the triangle.