A, B and C are the three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 900 and 1100 respectively.Find the angle BAC. A, B और C एक वृत्त पर स्थित तीन बिंदु ऐसे हैं कि जीवा AB और AC द्वारा केंद्र O पर बनाए गए कोण क्रमशः 900 और 1100 हैं | कोण BAC का मान ज्ञात कीजिये |

The angle at the center subtended by chord AB is 90°, and by chord AC is 110°. Therefore, angle AOC (where O is center) = 110° - 90° = 20°. The angle subtended by an arc at the center is twice the angle at any point on the remaining circumference. Therefore, ∠BAC = (1/2) × ∠BOC, where ∠BOC = 360° - 110° - 90° = 160° (or equivalently, the reflex angle). However, using the property that the angle between two chords equals half the difference of the arcs they subtend: ∠BAC = (1/2) × (arc BC not containing A). Given central angles of 90° and 110°, the angle at the circumference BAC = (1/2) × (110° - 90°) × 2 = 80° (considering the geometric configuration where A, B, C are on the circle in that order).