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520. Given triangle ABC, let F be the point where segment BC meets the bisector of angle BAC, Draw the line through B that is parallel to segment AF, and let E be the point where this parallel me...
Given a triangle ABC, let l_1 be the angle bisector of <A and let l_2 be...
Given a triangle ABC, let l_1 be the angle bisector of <A
and let l_2 be the perpendicular bisector of line BC. Assuming AB
> AC, show that l_1 intersection l_2 is not in triangle
ABC
Excuse l_2 is the perpendicular bisector of line BC hence the right
angle. The questions is to show a step by step proof that when l_1
abd l_2 intersect, it will be outside of the given triangle.
Given a triangle ABe, let Libe the...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denot...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
23.4 Let ABC be any triangle, let DE be a line parallel to the base, and let F be any point on DE. Show that the area of the union of the two triangles DBF and ECF is less than or equal to one-fourth...
23.4 Let ABC be any triangle, let DE be a line parallel to the base, and let F be any point on DE. Show that the area of the union of the two triangles DBF and ECF is less than or equal to one-fourth the area of the whole triangle, with equality if and only if D and E are the midpoints of AB and AC.
23.4 Let ABC be any triangle, let DE be a line parallel to the...
Given a triangle ABC, let l_1 be the angle bisector of <A
and let l_2 be the perpendicular bisector of line BC. Assuming AB
> AC, show that l_1 intersection l_2 is not in triangle
ABC
Excuse l_2 is the perpendicular bisector of line BC hence the right
angle. The questions is to show a step by step proof that when l_1
abd l_2 intersect, it will be outside of the given triangle.
Given a triangle ABe, let Libe the...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
23.4 Let ABC be any triangle, let DE be a line parallel to the base, and let F be any point on DE. Show that the area of the union of the two triangles DBF and ECF is less than or equal to one-fourth the area of the whole triangle, with equality if and only if D and E are the midpoints of AB and AC.
23.4 Let ABC be any triangle, let DE be a line parallel to the...
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