Q1. [1] § 10.4 Summary
In the given figure, 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 $\angle MON$ is :
- A $120°$
- B $140°$
- C $70°$
- D $90°$
Previously asked in CBSE board exam
2024 30/3/1 Q18
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
Option B: 140°
By the tangent-chord angle theorem, ∠OML = 90° (radius ⊥ tangent). So ∠OMN = 90° − 70° = 20°. Since OM = ON (radii), ∠ONM = 20°, giving ∠MON = 180° − 20° − 20° = 140°.
Explanation
- The tangent is perpendicular to the radius at the point of contact (Theorem 10.1), so ∠OML = 90°.
- The angle between the chord and the radius OM = 90° − 70° = 20°.
- Triangle OMN is isosceles (OM = ON = radii), so both base angles are 20°.
- Central angle = 180° − 20° − 20° = 140°.
- Examiners expect you to use the tangent-radius perpendicularity property and isosceles triangle reasoning clearly.
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