8_2
8_2
Solution:
Construct the triangle ABC with the vertex A being the origin. Then, construct the angle bisector BCA. Next, construct perpendicular lines through B perpendicular to b and through A perpendicular to A. Construct as the point that intersects the line through D perpendicular to b. Construct the point H (orthocenter).
a- as you can see the x coordinate of B is h.
b- As you can see the point C =()
c- angel bisector theorem shown
8_2
Consider the problem of construction of triangle ABC from the vertex A, the orthocenter H, and the trace T_b of the bisector of angle B. Put the origin at A, and let Tb = (a, 0), H = (h, k).
(a) Show that the x-coordinate of B is h.
(b) Suppose B = (h, q). Show that C is the point
(c) Use the angle bisector theorem to show that