KVPY SA Exam 2015 Question Paper

Question : 6 of 80

Marks: +1, -0

In a triangle ABC, points X and Y are on AB and AC, respectively, such that XY is parallel to BC. Which of the. two following equalities always hold? (Here [PQR] denotes the area of triangle PQR.)
(I) [BCX] = [BCY].
(II) [ACX]. [ ABY] = [AXY] . [ABC].

Neither (I) nor (II)
(I) only
(II) only
Both (I) and (II)

Validate

Solution:

Clearly ar (BCX) = ar (BCY) {∆s between parallel lines & same base}
⇒ [BCX] = [BCY]
(I) is true.
Check
(II) ar (∆ ACX) =

1/2

AC.AX sin A
ar(∆ABY) =

1/2

AB.AY sin A.
ar (∆AXY) =

1/2

AX.AY sin A
ar (∆ABC) =

1/2

AB.AC sin A.
Clearly [ACX].[ABY] = [AXY].[ABC]
(II) is true.

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