Given-that-ABCD-is-a-trapezium-such-that-AD-BC-The-centroid-of-ABD-lies-on-the-bisector-of-BCD-Show-that-the-centroid-of-ABC-lies-on-the-bisector-of-ADC-

Tinku Tara October 26, 2023 Geometry 0 Comments

Question Number 199006 by adhigenz last updated on 26/Oct/23

Given that ABCD is a trapezium such that AD//BC. The centroid of △ABD lies on the bisector of ∠BCD. Show that the centroid of △ABC lies on the bisector of ∠ADC.

$$\mathrm{Given}\:\mathrm{that}\:{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium}\:\mathrm{such}\:\mathrm{that}\:{AD}//{BC}. \\ $$$$\mathrm{The}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABD}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{BCD}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABC}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{ADC}. \\ $$

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Given-that-ABCD-is-a-trapezium-such-that-AD-BC-The-centroid-of-ABD-lies-on-the-bisector-of-BCD-Show-that-the-centroid-of-ABC-lies-on-the-bisector-of-ADC-

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