MathDB

Suppose that

A_1A_2A_3

is a triangle with

A_1A_2 = 16

and

A_1A_3 = A_2A_3 = 10

. For each integer

n \ge 4

, set An to be the circumcenter of triangle

A_{n-1}A_{n-2}A_{n-3}

. There exists a unique point

Z

lying in the interiors of the circumcircles of triangles

A_kA_{k+1}A_{k+2}

for all integers

k \ge 1

. If

ZA^2_1+ ZA^2_2+ ZA^2_3+ ZA^2_4

can be expressed as

\frac{a}{b}

for positive integers

a, b

with

gcd(a, b) = 1

, find

a + b

Problem Statement