Question

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

• A. 4
• B. 8
• C. 6
• D. 5

Answer 1

The correct option is C

6

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 $\Delta MON$,

OX = OM = radius of the circle
OY = ON = radius of the circle
$\angle XOY=\angle MON={85}^{\circ }$ (given)
$\therefore \Delta XOY\cong \Delta MON$ (by SAS similarity criterion)

$\therefore XY=MN$ (C.P.C.T)

$⟹MN=XY=6cm$.