Saturday, June 15, 2013

Problem 889: Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius

Geometry Problem. GeoGebra, HTML5 Animation for iPad and Nexus.
Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the dynamic geometry demostration of problem 889.

Online Geometry Problem 889: Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra

Posted by Antonio Gutierrez at 8:43 AM
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2 comments:

  1. Jacob HA (EMK2000)June 15, 2013 at 7:28 PM

    OA1 + OB1 + OC1
    = R (cosA + cosB + cosC)
    = R (1 + 4 sinA/2 sinB/2 sinC/2)
    = R + 4R sinA/2 sinB/2 sinC/2
    = R + r

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  2. Jacob HA (EMK2000)June 16, 2013 at 1:40 AM

    The last step follows from

    r (cotB/2 + cotC/2) = a = 2R sinA = 4R sinA/2 cosA/2
    r = 4R sinA/2 sinB/2 sinC/2

    ReplyDelete

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