Question

In the fig; we have X and Y are the mid-points of AC and BC and $AX=CY$, then

• A. $AC=BC$
• B. $AB=BC$
• C. $AC=AB$
• D. $CX=CY$

Answer 1

Answer: (A), (D)

The correct options are
A $AC=BC$
D $CX=CY$

Given: $X$ is mid point of $AC$ and $Y$is mid point of $BC$, $AX=CY$
$X$ is mid point of $AC$
$AX=CX$ (1)
$Y$ is mid point of $BC$
$CY=BY$ (2)
Also, given, $AX=CY$ (3)
Hence, from (1), (2) and (3)
$AX=CX=CY=BY$
$2AX=2BY$
$AC=BC$