Question

Three parallel lines are such that one passes through each vertex of a triangle ABC, and they are not parallel to any of the triangles sides. The line through A meets BC (extended if necessary) in X, the lines through B and C meet CA and AB in Y and Z respectively. Prove that area(XYZ) = 2xArea(ABC)

Answer #1

5. Suppose that the incenter I of ABC is on the triangle’s Euler
line. Show that the triangle is isosceles.
6. Suppose that three circles of equal radius pass through a
common point P, and denote by A, B, and C the three other points
where some two of these circles cross. Show that the unique circle
passing through A, B, and C has the same radius as the original
three circles.
7. Suppose A, B, and C are distinct...

Let J be a point in the interior of triangle ABC. Let D, E, F be
the feet of the perpendiculars from J to BC, CA, and AB,
respectively. If each of the three quadrilaterals AEJF, BFJD, CDJE
has an inscribed circle tangent to all four sides, then J is the
incenter of ∆ABC. It is sufficient to show that J lies on one of
the angle bisectors.

1. This exercise asks you to
negate various results that are equivalent to the Euclidean
parallel postulate.
(a) Alternate Postulate 5.1. Given a line and a
point not on the line, exactly one line can be drawn through the
given point and parallel to the given line.
(b) Alternate Postulate 5.2. If two parallel lines
are cut but a transversal, then the alternate interior angles are
equal, each exterior angle is equal to the opposite interior angle,
and sum of...

∠ABC is a right angle. AB = 8 inches,
BC = 13 inches, and AD = 3 feet. Determine the
surface area (in square inches) and volume (in cubic inches) of the
following. (Round your answers to one decimal place.)
A triangular prism is given. The prism is oriented so that the
top and bottom faces are triangles. Four vertices of the prism are
labeled as follows:
The bottom left vertex of the top triangular face is labeled
A.
The...

What tools could AA leaders have used to increase their
awareness of internal and external issues?
???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

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