Need no geometric property

Geometry Level 5

Let I , H , O I,H,O be the incenter, centroid, and circumcenter of the nonisosceles triangle A B C ABC .

If A I ∥ H O AI \parallel HO , find ∠ B A C \angle BAC in degrees.


The answer is 120.

Priyanshu Mishra by Priyanshu Mishra , 20, India

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1 solution

Ahmad Saad
Nov 12, 2016

2 Helpful 1 Interesting 0 Brilliant 0 Confused

Please correct the typos: G is the centroid (in the problem statement, this is given as H), O is the circumcentre, I is the incentre, Tr. OBD is 30°- 60°- 90° (Tr. OBE is 30° -30°-120°). Nice solution. Mr. Ahmad Sad!

Ajit Athle - 4 years, 7 months ago

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I have changed symbol "H" to "G" as a centroid, which famously located that "H" is an orthocenter and "G" is a centroid.

Ahmad Saad - 4 years, 7 months ago

Please elaborate your solution more. This is IMO 1991 LONGLISTED problem.

Priyanshu Mishra - 4 years, 7 months ago

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what details you want ?

Ahmad Saad - 4 years, 7 months ago

Nice solution sir!

Anmol Shetty - 4 years ago

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