Wednesday, August 31, 2011

Geometry Problem 662: Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 662.

Geometry Problem 662: Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement.

Posted by Antonio Gutierrez at 3:36 PM
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2 comments:

  1. PravinAugust 31, 2011 at 5:53 PM

    ∠ADC = ∠AEC
    ⇒ 180° - B = B + A/2 + C/2
    ⇒ 180° - B = 90° + B/2
    ⇒ 3B/2 = 90 °
    ⇒ B = 60°
    ⇒ ∠AFC = 120°

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  2. Peter TranAugust 31, 2011 at 9:02 PM

    Since D is the orthocenter of tri. ABC so angle (ADC)=180- angle (B)
    Since E is the incenter of tri. ABC so angle (AEC)=B + (A+C)/2
    We have 180-B=B+(A+C)/2
    Replace (A+C)/2= 90- B/2 in above expression
    We get B= 60 and angle (AFC)=120
    Peter Tran

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