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Given any triangle ABC, the signed sum of perpendicular distances from the circumcenter O to the sides (i.e., signed lengths of the pedal lines from O) is OO_A+OO_B+OO_C=R+r, ...

Inscribe a triangle in a circle such that the sides of the triangle pass through three given points A, B, and C.

A leg of a right triangle (i.e., a side adjacent the right angle) is also known as a cathetus (plural: catheti). While this usage is rather rare in English, the terms ...

A central circle is a circle with trilinear equation (lalpha+mbeta+ngamma)(aalpha+bbeta+cgamma)+k(abetagamma+bgammaalpha+calphabeta)=0 such that l:m:n is a triangle center ...

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

Let a, b, and c be the side lengths of a reference triangle DeltaABC. Now let A_b be a point on the extension of the segment CA beyond A such that AA_b=a. Similarly, define ...

Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

An n-gonal cupola Q_n is a polyhedron having n obliquely oriented triangular and n rectangular faces separating an {n} and a {2n} regular polygon, each oriented horizontally. ...

The Dou circle is the circle cutting the sidelines of the reference triangle DeltaABC at A^', A^(''), B^', B^(''), C^', and C^('') such that ...