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24 Cards in this Set
- Front
- Back
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A polygon is cyclic iff... |
there exists a circle that contains all of its vertices. |
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Every triangle is...
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cyclic. |
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circumcircle
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The circle that intersects all of the vertices of a triangle. |
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circumcenter |
The center of the circumcircle.
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A polygon is inscribed in a circle iff... |
each vertex of the polygon lies on the circle. |
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The circle that contains each vertex of a polygon is said to be... |
circumscribed about the polygon. |
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The perpendicular bisectors of the sides of a triangle...
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are concurrent. These define the circumcenter. |
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A quadrilateral is cyclic iff...
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a pair of its opposite angles are supplementary. |
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A circle is inscribed in a polygon iff...
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each side of the polygon is tangent to the circle. |
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If a circle is inscribed in a polygon, then...
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the polygon is said to be circumscribed about the circle. |
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A circle inscribed in a polygon is called...
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the incircle, and its center is called the incenter. |
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The angle bisectors of a triangle...
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are concurrent. This point is called the incenter. |
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A median of a triangle is...
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a line segment that joins a vertex to the midpoint of the opposite side. |
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The medians of a triangle...
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are concurrent. This point is called the centroid. |
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The centroid of a triangle is...
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the point in which its medians are concurrent. |
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The lines containing the altitudes of a triangle...
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are concurrent. This point is called the orthocenter. |
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The orthocenter of a triangle is...
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the point in which the lines containing its altitudes are concurrent. |
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The cevian of a triangle is...
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a line segment that joins a vertex of the triangle to a point on the opposite side. |
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Three cevians, AY, BZ, and CX of triangle ABC are concurrent iff... |
(AX / XB) * (BY / YC) * (CZ / ZA) = 1 |
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The circle that intersects all of the vertices of a triangle. |
circumcircle |
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The center of the circumcircle. |
circumcenter |
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If each vertex of a polygon lies on a circle, then... |
the polygon is circumscribed by the circle. |
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If a pair of opposite angles of a quadrilateral are supplementary, then... |
the quadrilateral is cyclic. |
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The incenter of a polygon is... |
the center of the incircle. |
