MathDB

Let

ABC

be a triangle. Construct three circles

k_1

k_2

, and

k_3

with the same radius such that they intersect each other at a common point

O

inside the triangle

ABC

and

k_1\cap k_2=\{A,O\}

k_2 \cap k_3=\{B,O\}

k_3\cap k_1=\{C,O\}

. Let

t_a

be a common tangent of circles

k_1

and

k_2

such that

A

is closer to

t_a

than

O

. Define

t_b

and

t_c

similarly. Those three tangents determine a triangle

MNP

such that the triangle

ABC

is inside the triangle

MNP

. Prove that the area of

MNP

is at least

9

times the area of

ABC

Problem Statement