The A-mixtilinear excircle (O ) can be easily constructed by noting that the polar of A passes through a the excenter Ia ; similarly for the other two mixtilinear excircles. See Figure 6. Theorem 9. If the mixtilinear excircles touch the circumcircle at X , Y , Z re- spectively...
mixtilinear excircles are defi ned analogously to the mixtilinear incircles except that the tangencies with the circumcircle are external The A mixtilinear excircle O a can be easily constructed by noting that the polar of A passes through the excenter Ia similarly for the other two mixti...
Abstract.Amixtilinearincircle(respectivelyexcircle)ofatriangleistangentto twosidesandtothecircumcircleinternally(respectivelyexternally).Westudy theconfigurationofthethreemixtilinearincircles(respectivelyexcircles).In particular,wegiveeasyconstructionsofthecircle(apartfromthecircumcircle) ...
A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one corresponding to each angle of the triangle. The radius of the -mixtilinear incircle inscribed in is given by (1) ...