Kindly solve the following problem Kindly solve the following problem (12 ) In the figure below. O is the centre Ofthe ein•le and AB is a diameter. C is a point on the circle. i) Compute LA ii) Draw another figure this, changing the size of Z_COB and a joined to another point on the circle, what would be the angle got? Share with your friends Share 2 Sanjay Kumar Manjhi answered this Dear Student,i) In △ABC;(Sum of all three angles of any triangle is 180°), So;∠CAB+∠ABC+∠ACB=180° ................(i)Given, ∠COB=50°So, ∠AOC=180°-∠COB⇒180°-50°=130°Now,Angle subtended by an arc at the centre is double the angle subtended by same arc at any point on the circle.So,∠CAB=12∠COB⇒∠CAB=12×50°⇒∠CAB=25°And similarly,∠ABC=12∠AOC⇒∠ABC=12×130°⇒∠ABC=65°Now from equation (i), we get;∠CAB+∠ABC+∠ACB=180°⇒25°+65°+∠ACB=180°⇒∠ACB=180°-(25°+65°)⇒∠ACB=90°ii) Suppose, ∠COB=60°In △ABC;(Sum of all three angles of any triangle is 180°), So;∠CAB+∠ABC+∠ACB=180° ................(i)Given, ∠COB=60°So, ∠AOC=180°-∠COB⇒180°-60°=120°Now,Angle subtended by an arc at the centre is double the angle subtended by same arc at any point on the circle.So,∠CAB=12∠COB⇒∠CAB=12×60°⇒∠CAB=30°And similarly,∠ABC=12∠AOC⇒∠ABC=12×120°⇒∠ABC=60°Now from equation (i), we get;∠CAB+∠ABC+∠ACB=180°⇒30°+60°+∠ACB=180°⇒∠ACB=180°-(30°+60°)⇒∠ACB=90°In any circle, if the ends of a diameter are joined to another point on the circle, the angle we got would be a right angle(90°). Regards 1 View Full Answer