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?

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°-COB180°-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=12COBCAB=12×50°CAB=25°And similarly,ABC=12AOCABC=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°-COB180°-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=12COBCAB=12×60°CAB=30°And similarly,ABC=12AOCABC=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
What are you looking for?