Geometry Problem

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

Click the figure below to see the complete problem 662.

## Wednesday, August 31, 2011

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

Labels:
angle,
circumcenter,
incenter,
orthocenter,
triangle

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∠ADC = ∠AEC

ReplyDelete⇒ 180° - B = B + A/2 + C/2

⇒ 180° - B = 90° + B/2

⇒ 3B/2 = 90 °

⇒ B = 60°

⇒ ∠AFC = 120°

Since D is the orthocenter of tri. ABC so angle (ADC)=180- angle (B)

ReplyDeleteSince 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