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tmua.me Extreme Set C Paper 2 · Q20

Paper 2Geometry

The vertices of a rectangle are A,B,C,DA,B,C,D, in that order, with

AB=23,BC=2.AB=2\sqrt3,\qquad BC=2.

A point PP in the plane of the rectangle satisfies

PA2+PC2=12.PA^2+PC^2=12.

What is the least possible value of

PA⋅PB⋅PC⋅PD ?PA\cdot PB\cdot PC\cdot PD\,?
A44
B1212
C636\sqrt3
D4134\sqrt{13}
E2828
F108108

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