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 area of the triangle formed by the lines $x + y - 3 = 0$,$x - 3y + 9 = 0$,and $3x - 2y + 1 = 0$ is:

In a $\triangle ABC$,$2x+3y+1=0$ and $x+2y-12=0$ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively. If $A$ is $(3,2)$,then the slope of the side $BC$ is

The equations of the sides $AB$,$BC$,and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 15a$,and $x - y = 3$ respectively. If its orthocentre is $(2, a)$,where $-\frac{1}{2} < a < 2$,then $p$ is equal to...

If the sides of a triangle are given by the equations $x + y - 5 = 0$,$x - y + 1 = 0$,and $y - 1 = 0$,then what is its circumcenter?

The circumcentre of the triangle formed by the lines $xy+2x+2y+4=0$ and $x+y+2=0$ 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$. $[ACX] \cdot [ABY] = [AXY] \cdot [ABC]$