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Regular Triangular Pyramid

Source: 1995 National High School Mathematics League, Exam One, Problem 6

March 3, 2020
geometry3D geometrypyramid

Problem Statement

OO is the center of the bottom surface of regular triangular pyramid P−ABCP-ABC. A plane passes OO intersects line segment PCPC at SS, intersects the extended line of PA,PBPA,PB at Q,RQ,R, then 1∣PQ∣+1∣PR∣+1∣PS∣\frac{1}{|PQ|}+\frac{1}{|PR|}+\frac{1}{|PS|} (A)\text{(A)} has a maximum value, but no minumum value (B)\text{(B)} has a minumum value, but no maximum value (C)\text{(C)} has both minumum value and maximum value (different) (D)\text{(D)} is a fixed value
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