Multiple choice

Let PQ be a tangent to a circle at point A and AB be a chord. Let C be a point on the circle such that ∠BAC = 54o and ∠BAQ = 62o. Find ∠ABC. माना PQ स्पर्श रेखा एक वृत्त के A बिन्दु पर है और AB एक जीवा है। माना बिन्दु C वृत्त पर इस प्रकार है कि ∠BAC = 54o और ∠BAQ = 62oतो ∠ABC ज्ञात कीजिए।\

  1. 62o

  2. 64o

  3. 60o

  4. 70o

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The angle between tangent and chord equals the angle in the alternate segment. So ∠BAQ = ∠BCA = 62°. In triangle ABC, angles sum to 180°: ∠BAC + ∠ABC + ∠BCA = 180°. Substituting: 54° + ∠ABC + 62° = 180°. Therefore, ∠ABC = 180° - 116° = 64°.