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 Problem 29. Right Triangle. Level: High School, SAT Prep, College geometry

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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Last updated: July 23, 2007