In triangle ABC, AD is a median and O is any point on AD. BO and CD on producing meet AC and

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#IntriangleABCADisamedianandOisanypointonAD
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In triangle ABC, AD is a median and O is any point on AD. BO and CD on producing meet AC and AB at E and F respectively. Now AD is produced to X such that CD=DX as shown in figure.
(i) EF || BC
(ii) AO : AX = AF : AB
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