Q. 65.0( 1 Vote )

In ΔABC, D and E are the mid-points of and respectively. and intersect in G. A line m passing through D and parallel to intersects in K. Prove that AC = 4CK.

Answer :

Given, In ABC, D and E are the mid-points of and respectively. and intersect in G. A line m passing through D and parallel to intersects in K


To prove : AC = 4CK


Proof : In ∆ABC, E is the midpoint of AC.


CE = AC


AC = 2CE ...... (i)


In ∆ABC, D is the midpoint of BC.


CD = CB


-...... (ii)


In ∆CBE, C-D-B, C-K-E



From eq (ii)



Hence, CE = 2CK


Substituting this into eq (i)


AC = 2 (2CK)


AC = 4CK


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