In ΔPQR, 
, 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 
Given, In 
PQR, 
, 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
To prove : 
Proof : In 
PQR, XY || PR
∴ 
...... (i)
In 
PQX, YZ || PX
∴ 
...... (ii)
From eq (i) and (ii),
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.
and 
such that 
|| 
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and 
respectively. 
and 
intersect in G. A line m passing through D and parallel to 
intersects 
in K. P
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.
in D and the bisector of
in E. Prove that AB × AD × EC = AC × BD × AE.