MathDB

A, B, and two excircles cyc

Source: 2004 Korea Junior Math Olympiad

June 28, 2024

geometryrectangleexcirclecyclic quadrilateral

Problem Statement

ABCD

is a cyclic quadrilateral inscribed in circle

O

. Let

O_1

be the

A

-excenter of

ABC

and

O_2

the

A

-excenter of

ABD

. Show that

A, B, O_1, O_2

is concyclic, and

O

passes through the center of

(ABO_1O_2)

.
Recall that for concyclic

X, Y, Z, W

, the notation

(XYZW)

denotes the circumcircle of

XYZW

.

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