Q1. [1] § 10.3 Number of Tangents from a Point on a Circle § 10.4 Summary
In the given figure, if PT is a tangent to a circle with centre O and $\angle TPO = 35°$, then the measure of $\angle x$ is :
- A $110°$
- B $115°$
- C $120°$
- D $125°$
Previously asked in CBSE board exam
2024 30/3/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
(D) 125°
Since OT ⊥ PT (radius ⊥ tangent), ∠OTP = 90°. In △OTP, ∠TOP = 180° − 90° − 35° = 55°. So ∠x = 180° − 55° = 125° (linear pair / reflex consideration: x = 90° + 35° = 125°).
Explanation
Key facts: (1) Tangent ⊥ radius at point of contact, so ∠OTP = 90°. (2) Angle sum in △OTP gives ∠POT = 55°. (3) Angle x (the obtuse/reflex angle at O on the other side) = 180° − 55° = 125°. Examiners expect you to use Theorem 10.1 and the angle-sum property of a triangle.
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