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In
triangle ABC,
angle B is a right angle, BD is the
altitude, O is the
incenter,
r is the
inradius, BE is the
bisector of angle ABD, BF is the
bisector of angle DBC. EO and FO are extended until they meet
sides BC and AB at H and G, respectively. Prove the following:
1. EF = 2r
2. M is the
midpoint of EF
3. OE = OF = OB =
4. O is the
circumcenter of triangle
BEF
5. Quadrilateral BHOG is
cyclic
6. OG = OH
7.EH and FG are congruent and
perpendicular
8. Angles A and BOH are congruent,
similarly C and BOG
9. GH is
parallel to AC
10. EG = FH
.
See solution below
Hints: See
Geometry Help
Mind Map: George Pólya's 1945 book,
"How to Solve It"
George Pólya's 1945 book "How to Solve It, A new aspect of
Mathematical Method", is a book describing methods of problem
solving. It suggests the following steps when solving a
mathematical problem: (1) First, you have to understand the
problem. (2) After understanding, then make a plan. (3) Carry
out the plan. (4) Look back on your work. How could it be
better?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.
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Altitude |
Circle Tangent Line
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Right triangle, Altitude and Incircle |
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| By Antonio Gutierrez
Post or view a solution to the problem 29
Last updated: Sep 19, 2014
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