Question

In the figure below A, B, C and D are points on the circumference of the circle, centre 0, A tangent to the circle at A intersects chord CD produced at E. Line AB is parallel to line EC. Angle AED = 45° and angle ABD = 40°.

1. Calculate the size of
   • <ADB. 
   • <OCD 
2. Given that ED = 3.5 cm and DC = 4.9 cm, calculate correct to 1 decimal place: 
   • the length of the tangent AE. 
   • the radius of the circle. 

Answer 1

1. 
   
   • <ADB = 45
   • <OCD = 35
2. 8.4 x 3.5=AE2
   • AE=±5.422
     ∴ AE = 5.422 ≈ 5.4
     r = 2.45  
          cos 35
     = 2.991
     ≈ 3.0 cm