MathDB

BMT 2022 Guts #24

Source:

August 31, 2023

geometry

Problem Statement

Let

\vartriangle BCD

be an equilateral triangle and

A

be a point on the circumcircle of

\vartriangle BCD

such that

A

is on the minor arc

BD

. Then, let

P

be the intersection of

\overline{AB}

with

\overline{CD}

,

Q

be the intersection of

\overline{AC}

with

\overline{DB}

, and

R

be the intersection of

\overline{AD}

with

\overline{BC}

. Finally, let

X

,

Y

, and

Z

be the feet of the altitudes from

P

,

Q

, and

R

, respectively, in triangle

\vartriangle PQR

. Given

BQ = 3 -\sqrt5

and

BC = 2

, compute the product of the areas

[\vartriangle XCD] \cdot [\vartriangle Y DB] \cdot [\vartriangle ZBC]

.

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