In the given figure, PQ is tangent to the circle centred at O. If $\angle AOB = 95°$, then the measure of $\a…

Question

In the given figure, PQ is tangent to the circle centred at O. If $\angle AOB = 95°$, then the measure of $\angle ABQ$ will be

Accepted Answer

## Model Answer **Option (A) 47.5°** OB ⊥ BQ (radius ⊥ tangent), so ∠OBQ = 90°. In △OAB, OA = OB (radii), so ∠OAB = ∠OBA = (180° − 95°)/2 = 42.5°. Therefore, ∠ABQ = 90° − 42.5° = **47.5°**. ## Explanation Key steps: (1) Tangent ⊥ radius at point of contact gives ∠OBQ = 90°. (2) Since OA = OB (radii), △OAB is isosceles, so ∠OBA = (180° − 95°)/2 = 42.5°. (3) ∠ABQ = ∠OBQ − ∠OBA = 90° − 42.5° = 47.5°. Examiners expect both the tangent-radius perpendicularity theorem and the isosceles triangle property to be applied.

Mathematics — CBSE Class 10 board question