In ΔABC, 
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.
Given, In 
ABC, 
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 as shown in figure.
To prove : CY2 = AC × CZ
Proof : In ∆ABC, XY || AB
∴ 
...... (i)
In ∆YBC, XZ || BY
∴ 
...... (ii)
From eq (i) and (ii)
∴ CY2 = AC × CZ
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and 
respectively. 
and 
intersect in G. A line m passing through D and parallel to 
intersects 
in K. P
, 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 
in D and the bisector of
in E. Prove that AB × AD × EC = AC × BD × AE.
and P is the mid-point of
. 
intersects 
in Q. Prove that (i) CQ = 2AQ (ii) BP = 3PQ