Question : In a triangle MNO, XA, XB, and XC are perpendicular bisectors on sides MN, ON, and OM respectively intersecting each other at X. If $\angle \mathrm{NMO}=55°$, then what is the value of $\angle \mathrm{NXO}$?
Option 1: 130°
Option 2: 110°
Option 3: 95°
Option 4: 125°
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Correct Answer: 110°
Solution :
$\angle NXO$ is the angle made at the circumcenter of the triangle.
⇒ $\angle NXO = 2 × ∠NMO$
⇒ $∠NXO = 2 × 55°$
⇒ $∠NXO = 110°$
Hence, the correct answer is 110°.
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