Cube-ABCD-EFGH-has-side-length-a-Point-P-lies-on-AC-such-that-AP-PC-3-1-Through-P-a-line-l-parallel-to-BD-is-drawn-such-that-l-each-intersect-BC-at-X-and-CD-at-Y-If-AC-and-BD-intersect-at-O

Question Number 146487 by syamilkamil1 last updated on 13/Jul/21

$$ \\ $$$$\mathrm{Cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{has}\:\mathrm{side}\:\mathrm{length}\:\mathrm{a}. \\ $$$$\mathrm{P}{o}\mathrm{int}\:\mathrm{P}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{AC}\:\mathrm{such}\:\mathrm{that}\:\mathrm{AP}\::\:\mathrm{PC}\:=\:\mathrm{3}\::\:\mathrm{1}\:\mathrm{Through}\:\mathrm{P}\:\mathrm{a}\:\mathrm{line}\:\mathrm{l}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{BD}\:\mathrm{is} \\ $$$$\mathrm{dr}{a}\mathrm{wn}\:\mathrm{such}\:\mathrm{that}\:\mathrm{l}\:\mathrm{each}\:\mathrm{intersect}\:\mathrm{BC}\:\mathrm{at}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{at}\:\mathrm{Y}.\:\mathrm{If}\:\mathrm{AC}\:\mathrm{and}\:\mathrm{BD}\: \\ $$$$\mathrm{intersect}\:\mathrm{at}\:\mathrm{O}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\: \\ $$$$\mathrm{between}\:\mathrm{XY}\:\mathrm{with}\:\mathrm{OG}! \\ $$

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