Question

In the fig., it is given that:
$XY=6cm$
$\angle XOY=\angle MON={85}^{\circ }$.
The length of the chord MN is ___cm.

• A. 4
• B. 8
• C. 6
• D. 5

Answer 1

The correct option is C 6

In the given question, it is given that $\angle XOY=\angle MON$.

If the angles subtended by the chords at the centre are equal then the two chords are of equal length.

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)

$⟹MN=XY=6cm$.