Chords AB, BC, CD subtend angles of 80o, 60o and 70o respectively at the center O of the circle then the acute angle between AC and BD is- जीवा AB, BC, CD जिनका केन्द्र O के साथ कोण क्रमशः 80o, 60o और 70o है तो AC और BD के मध्य न्यून कोण होगा ?
B
Correct answer
Explanation
Angles subtended by equal chords are equal. Let angle AOB = 80°, BOC = 60°, COD = 70°. Then AOC = AOB + BOC = 140° and BOD = BOC + COD = 130°. Let AC and BD intersect at P. In triangle APB: angle APB = 180° - angle PAB - angle PBA = 180° - 70° - 65° = 45°. The acute angle between AC and BD is angle APB + angle BPC (vertically opposite) = 45° + 30° = 75°. Alternatively, using angle bisector properties at intersection P.