Question

In the figure, $XY=6cm,\angle XOY=\angle MON={85}^{\circ }$. The length of the chord $MN$ is

• A. 4
• B. 8
• C. 6
• D. 5

Answer 1

The correct option is C 6

It is given that $\angle XOY=\angle MON$.

Consider $\Delta XOY$ and $\Delta MON$,

Here,

$OX=OM=$ radius of the circle

$OY=ON=$ radius of the circle

and $\angle XOY=\angle MON={85}^{\circ }$ [given]

$\therefore \Delta XOY\cong \Delta MON$ [by SAS criterion]

$\therefore XY=MN$ [CPCT]

$\Rightarrow MN=XY=6cm$.