MCQ 511 Mark
In $\triangle\text{ABC},$ a line $\text{XY}$ parallel to $\text{BC}$ cuts $\text{AB}$ at $\text{X}$ and $\text{AC}$ at $Y.$ If $\text{BY}$ bisects $\angle\text{XYC},$ then:
- ✓$\text{BC} = \text{CY}$
- B$\text{BC} = \text{BY}$
- C$\text{BC}\neq\text{ CY}$
- D$\text{BC}\neq\text{ BY}$
Answer
View full question & answer→Correct option: A.
$\text{BC} = \text{CY}$
Given: $\ce{XY \| BC}$ and $\text{BY}$ is bisector of $\angle\text{XYC}.$
Since $\ce{XY \| BC}$
So, $\angle\text{YBC}=\angle\text{BYC} ($Alternate angles$)$
Now, in triangle $\text{BYC}$ two angles are equal.
Therefore, the two corresponding sides will be equal.
Hence, $\text{BC = CY}$
Hence option $(a)$ is correct.
Since $\ce{XY \| BC}$
So, $\angle\text{YBC}=\angle\text{BYC} ($Alternate angles$)$
Now, in triangle $\text{BYC}$ two angles are equal.
Therefore, the two corresponding sides will be equal.
Hence, $\text{BC = CY}$
Hence option $(a)$ is correct.