Tuesday, December 8, 2009

Problem 400. Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence

Proposed Problem
Click the figure below to see the complete problem 400 about Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Problem 400. Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.
See also:
Complete Problem 400
Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 8:42 PM
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7 comments:

  1. |OG|=|OH|
    |OC|=|OD|=r
    |GC|=|DH|

    ReplyDelete

  3. suggest to others

    1) draw HP perpendicular to AC ( P on AC )
    2) draw OK perpendicular to HG ( K on HG )

    about first comment: step 1 and step 2 are not enough for step 3

    ReplyDelete

  4. reason for step 1:
    http://i49.tinypic.com/69omdj.gif

    and
    step 1 and step 2 are enough for step 3, i think

    ReplyDelete

  6. W/o having to refer to any other figure or any construction, we can easily see that quad. OFCE is concyclic and hence ang. HOG = ang. C while ang. OGH = ang. EGC = 90-C/2. Therefore, ang. OHG = 180 – C - (90-C/2)= 90 – C/2 or ang. OHG = ang. OGH. Hence etc.
    Ajit

    ReplyDelete

  7. step 1 and 2 need third condition of congruence,
    angle DOH = angle COG ? verify please

    my solution
    to draw OK perpendicular to HG give
    1) OK is median => HK = KG
    2) OK is diameter perpendicular to chord DC => DK=KC
    so DH=DK-HK
    and GC=KC-KG

    ReplyDelete

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