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.
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
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
in D. Prove that
and 
.
and 
such that 
|| 
.
.
, such that Q-X-R. A line parallel to 
and passing through X intersects 
in Y. A line parallel to px and passing through Y intersects 
in Z. Prove that 
and B-X-C. A line passing through X and parallel to 
intersects 
in Y. A line passing through X and parallel to 
intersects 
in Z. Prove that CY2 = AC • CZ.