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

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

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

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