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If {P} divides {O}{A} internally in the ratio _{{1}}:_{{2}} an

Question

If $P$ divides $O A$ internally in the ratio $λ_{1} : λ_{2}$ and $Q$ divides $O A$ externally in the ratio $λ_{1}; λ_{2},$ then prove that $O A$ is the harmonic mean of $O P$ and $O Q ˙$

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William Discussed

P

divides

O A

internally in the ratio

λ_{1} : λ_{2}

and

Q

divides

O A

externally in the ratio

λ_{1}; λ_{2},

then prove that

O A

is the harmonic mean of

O P

and

O Q ˙

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Question Text

P

divides

O A

internally in the ratio

λ_{1} : λ_{2}

and

Q

divides

O A

externally in the ratio

λ_{1}; λ_{2},

then prove that

O A

is the harmonic mean of

O P

and

O Q ˙

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