In a triangle ABC, the incircle touches the sides AB and AC at M and N respectively. If the centre of the circle is O and \angle A=70^{\circ}, then what is \angle MON equal to?

Explanation

The radii OM and ON are perpendicular to the tangents AB and AC, meaning \angle AMO = \angle ANO = 90^\circ. In quadrilateral AMON, the sum of angles is 360^\circ. Thus, \angle MON = 360^\circ - 90^\circ - 90^\circ - 70^\circ = 180^\circ - 70^\circ = 110^\circ.

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