MathDB

2021 Team #7

Source:

June 27, 2021

geometrytangencyCeva s theorem

Problem Statement

In triangle

ABC

, let

M

be the midpoint of

BC

and

D

be a point on segment

AM

. Distinct points

Y

and

Z

are chosen on rays

\overrightarrow{CA}

and

\overrightarrow{BA}

, respectively, such that

\angle DYC=\angle DCB

and

\angle DBC=\angle DZB

. Prove that the circumcircle of

\Delta DYZ

is tangent to the circumcircle of

\Delta DBC

.

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