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Suppose that the incircle of triangle ABC touches AB at Z, BC at X, and AC...

Suppose that the incircle of triangle ABC touches AB at Z, BC at X, and AC at Y . Show that AX, BY , and CZ are concurrent.

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Answer #1

A set of lines or curves are said to be concurrent if they all intersect. at the same point. In the figure below, the threelines are concurrent because they all intersect at a single point P. The point P is called the "point of concurrency".

BC can be shown perpendicular to AX and so on Therefore solve for altitude Let A(x1,y1) B(x2,y2) and C(x3,y3) be the vertices of the triangle ABC. If m1 is the slope of AB, then we use the two point formula to find the slope of the line m1.

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