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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
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