Question

In the figure below,P,Q,R and S are points on the circle centre O. PRT and USTV are straight lines.Line UV is a tangent to the circle at S. <RST= 500 and <RTV=1500.

Calculate the size of

1. < ORS
2. <USP 
3. < PQR 
4. Given that RT=7cm and ST=9cm,calculate to 3 significant figures
   • Length of the line PR 
   • The radius of the circle. 
      

Answer 1

1. < ORS = 40º
2. <USP =80º(50 +30)
3. < PQR=180º -50º=130º
4. Given that RT=7cm and ST=9cm,calculate to 3 significant figures
   • Length of the line PR 
     • (ST)2=PT:RT
       (9)2=PT=7cm
       PT=81/7=11.6(3s.f)
       11.6 - 7= 4.6
        
   • The radius of the circle. 
     4.6=    2R    
             Sin 500
     =3.00