Class X Session 2023-24 Question 9

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041) 

Question 9 

If O is centre of a circle and Chord PQ makes an angle 50° with the tangent PR at the point of contact P, then the angle subtended by the chord at the centre is

(a) 130°  (b) 100°                                                              

(c) 50°    (d) 30°

Explanation : 

OP ⊥ PR   [..it indicates that the line segment 𝑂𝑃 is perpendicular to the line 𝑃𝑅]

∠OPQ = 90° – 50° = 40°

OP = OQ   ...[Radii]

∴ ∠OPQ = ∠OQP = 40°

In ΔOPQ,

 ∠POQ + ∠OPQ + ∠OQP = 180° [..applied the angle sum property]

 ∠POQ + 40° + 40° = 180°

 ∠POQ = 180° – 80° = 100°

Guess the Option and comment below  👇