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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