MathDB

(MKT) is tangent to (ABC)

Source: 2021 Saudi Arabia Training Lists p17 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 6, 2022

geometrytangent circlescircumcircle

Problem Statement

Let

ABC

be an acute, non-isosceles triangle with circumcenter

O

. Tangent lines to

(O)

B,C

meet at

T

. A line passes through

T

cuts segments

AB

D

and cuts ray

CA

E

. Take

M

as midpoint of

DE

and suppose that

MA

cuts

(O)

again at

K

. Prove that

(MKT)

is tangent to

(O)