MathDB

Tangency of circles

Source: Iran TST 2007, Day 3

May 23, 2007

geometrycircumcirclegeometry proposed

Problem Statement

O

is a point inside triangle

ABC

such that

OA=OB+OC

. Suppose

B',C'

be midpoints of arcs \overarc{AOC} and

AOB

. Prove that circumcircles

COC'

and

BOB'

are tangent to each other.

Back to Problems View on AoPS