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Solution


Q.

In Fig, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70° with MN. The measure of ∠MON is:
1 120°  
2 140°  
3 70°  
4 90°  

Ans.

(2)

As ML is tangent at M and OM is radius of the circle, therefore ∠OML = 90°

⇒ ∠OMN + ∠NML = 90°
⇒ ∠OMN + 70° = 90° ⇒ ∠OMN = 20°

In ΔOMN, we have OM = ON (? radii of circle)
⇒ ∠OMN = ∠ONM = 20° (Angles opposite to equal sides are equal)

Also, ∠OMN + ∠MON + ∠ONM = 180°
⇒ 20° + ∠MON + 20° = 180°
⇒ ∠MON = 180° – 40° = 140°