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Question Number 17273 by VEGAMIND last updated on 03/Jul/17

The intersection of the ABC triangle  median is at G point. The corner  of the BGC is 90°. If the AG cut   length is 12 cm, locate the BC side.

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{intersection}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ABC}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{median}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{G}}\:\boldsymbol{\mathrm{point}}.\:\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{corner}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{BGC}}\:\boldsymbol{\mathrm{is}}\:\mathrm{90}°.\:\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{AG}}\:\boldsymbol{\mathrm{cut}}\: \\ $$$$\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{is}}\:\mathrm{12}\:\boldsymbol{\mathrm{cm}},\:\boldsymbol{\mathrm{locate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{BC}}\:\boldsymbol{\mathrm{side}}. \\ $$

Commented by 1234Hello last updated on 03/Jul/17

Is G the centroid of ΔABC?

$$\mathrm{Is}\:{G}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\Delta{ABC}? \\ $$

Commented by VEGAMIND last updated on 03/Jul/17

yes

$$\boldsymbol{\mathrm{yes}} \\ $$

Answered by ajfour last updated on 03/Jul/17

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