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

Question

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

Quantrex Academy · Accepted Answer

Correct answer: D. both (I) and (II)

BCX = BCY (Obvious) Same base and same height Now Let A ( O ), AB = b , AC = c So AX = b , AY = c ACX = 1 2 | b c | array l ABY = 1 2 | b c | AXY = 1 2 ²| b c | ABC = 1 2 | b c | array

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

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