MathDB

1

Part of 2011 India Regional Mathematical Olympiad

Problems(2)

Indian RMO 2011: Question 1

Source:

12/4/2011
Let ABCABC be a triangle. Let D,E,FD, E, F be points respectively on the segments BC,CA,ABBC, CA, AB such that AD,BE,CFAD, BE, CF concur at the point KK. Suppose BDDC=BFFA\frac{BD}{DC} = \frac {BF}{FA} and ∠ADB=∠AFC\angle ADB = \angle AFC. Prove that ∠ABE=∠CAD\angle ABE = \angle CAD.
AO and HM meet on odot(ABC) - [RMO2, India]

Source: 0

12/31/2011
Let ABCABC be an acute angled scalene triangle with circumcentre OO and orthocentre H.H. If MM is the midpoint of BC,BC, then show that AOAO and HMHM intersect on the circumcircle of ABC.ABC.
geometrycircumcircleincentertrigonometryparallelogramEulergeometric transformation