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max angle, altitude tangent to circumcircle (2011 NZOMC Camp Sel. S2)

Source:

January 4, 2021

geometrycircumcirclealtitudeangleangles

Problem Statement

In triangle

ABC

, the altitude from

B

is tangent to the circumcircle of

ABC

. Prove that the largest angle of the triangle is between

90^o

and

135^o

. If the altitudes from both

B

and from

C

are tangent to the circumcircle, then what are the angles of the triangle?