In a rectangle A B C D ABCD A BC D , points P P P and Q Q Q are on side B C BC BC such that the areas of triangles A B P ABP A BP , A P Q APQ A PQ , a...

Question

In a rectangle

ABCDABCD
, points
PP
and
QQ
are on side
BCBC
such that the areas of triangles
ABPABP
,
APQAPQ
, and
AQCAQC
are in geometric progression (GP). If the area of quadrilateral
AQCDAQCD
is four times the area of triangle
ABPABP
, then the ratio of
BP:PQ:QCBP : PQ : QC
is

Options

A.

1 : 2 : 4

B.

2 : 4 : 1

C.

2 : 1 : 4

D.

4 : 2 : 1

cat 2023ratiosgeometric progressionarea proportions

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