MathDB

2021 Geo Div 1 P6

Source:

March 2, 2021

geometry

Problem Statement

Let circles

\omega

and

\Gamma

, centered at

O_1

and

O_2

and having radii

42

and

54

respectively, intersect at points

X,Y

, such that

\angle O_1XO_2 = 105^{\circ}

. Points

A

,

B

lie on

\omega

and

\Gamma

respectively such that

\angle O_1XA = \angle AXB = \angle BXO_2

and

Y

lies on both minor arcs

XP

and

XB

. Define

C

to be the intersection of

\frac{AC}{BC}

and

BO_1

. Suppose

XP

intersects

AB

at

C

. What is the value of

\frac{AC}{BC}

?
Proposed by Puhua Cheng

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