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{A}{B}{C}{D} is a tetrahedron and {O} is any point. If the lin

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$A B C D$ is a tetrahedron and $O$ is any point. If the lines joining $O$ to the vrticfes meet the opposite faces at $P, Q, R a n d S,$ prove that $\frac{O P}{A P} + \frac{O Q}{B Q} + \frac{O R}{C R} + \frac{O S}{D S} = 1 .$

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A B C D

is a tetrahedron and

O

is any point. If the lines joining

O

to the vrticfes meet the opposite faces at

P, Q, R a n d S,

prove that

\frac{O P}{A P} + \frac{O Q}{B Q} + \frac{O R}{C R} + \frac{O S}{D S} = 1 .

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Question Text

A B C D

is a tetrahedron and

O

is any point. If the lines joining

O

to the vrticfes meet the opposite faces at

P, Q, R a n d S,

prove that

\frac{O P}{A P} + \frac{O Q}{B Q} + \frac{O R}{C R} + \frac{O S}{D S} = 1 .

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