In a triangle ABC,points X and Y are on AB an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The correct option is $(d)$.$I$. Since $	riangle BCX$ and $	riangle BCY$ share the same base $BC$ and lie between the same parallel lines $XY$ a

Vedclass · Accepted Answer

Both $I$ and $II$

Vedclass · Answer

(D) The correct option is $(d)$.$I$. Since $	riangle BCX$ and $	riangle BCY$ share the same base $BC$ and lie between the same parallel lines $XY$ and $BC$,their areas are equal. Thus,$[BCX] = [BCY]$ is true.$II$. Using the area formula $	ext{Area} = \frac{1}{2} ab \sin C$:$[ACX] = \frac{1}{2} (AX)(AC) \sin A$$[ABY] = \frac{1}{2} (AY)(AB) \sin A$$[ACX] \cdot [ABY] = \left( \frac{1}{2} (AX)(AC) \sin A ight) \cdot \left( \frac{1}{2} (AY)(AB) \sin A ight)$$= \left( \frac{1}{2} (AX)(AY) \sin A ight) \cdot \left( \frac{1}{2} (AB)(AC) \sin A ight)$$= [AXY] \cdot [ABC]$Thus,$II$ is also true.Therefore,both $I$ and $II$ are true.

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 $\triangle PQR$).
$I$. $[BCX] = [BCY]$
$II$. $[ACX] \cdot [ABY] = [AXY] \cdot [ABC]$

Similar Questions

The triangle with vertices $A(2, 4)$,$B(2, 6)$,and $C(2 + \sqrt{3}, 5)$ is a . . . .

Suppose a triangle is formed by $x+y=10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers,lying inside the triangle is

If the incentre of the triangle formed by the lines $x-2=0$,$x+y-1=0$,and $x-y+3=0$ is $(\alpha, \beta)$,then $\beta=$

If the points of intersection of the coordinate axes and $|x+y|=2$ form a rhombus,then its area is

Straight lines $x-y=7$ and $x+4y=2$ intersect at $B$. Points $A$ and $C$ are so chosen on these two lines such that $AB=AC$. The equation of line $AC$ passing through $(2,-7)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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$. $[ACX] \cdot [ABY] = [AXY] \cdot [ABC]$