If O is the centre of a circle and AB is a chord of the circle at a distance half of the radius of circle from the centre O.Find the value of the ∠BAO. यदि एक वृत्त का केंद्र O है तथा इसमें एक जीवा AB हैं जिसकी केंद्र O से दूरी वृत्त की त्रिज्या से आधी हैं। ∠BAO का मान ज्ञात कीजिए।

Let M be the midpoint of chord AB. In right triangle OMA: OM = r/2 (given, half the radius), OA = r (radius). Using trigonometry: cos(∠AOM) = OM/OA = (r/2)/r = 1/2, so ∠AOM = 60°. Since OM is perpendicular to AB, ∠BAO = 90° - 60° = 30°. This uses the property that the line from the center to a chord's midpoint is perpendicular to the chord.