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Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

A simple polygon with precisely two ears and one mouth.

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

The anticomplementary circle is the circumcircle of the anticomplementary triangle. It has radius R_A=2R, where R is the circumradius of the reference triangle, and center at ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

If P is a point on the circumcircle of a reference triangle, then the line PP^(-1), where P^(-1) is the isogonal conjugate of P, is called the antipedal line of P. It is a ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

The greatest radial distance of an ellipse as measured from a focus. Taking v=pi in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the apoapsis distance r_+=a(1+e). ...

The inverse curve of the Archimedean spiral r=atheta^(1/n) with inversion center at the origin and inversion radius k is the Archimedean spiral r=k/atheta^(-1/n).

Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...