ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Find value of  
AE
AD
 .


Answer:

1

Step by Step Explanation:
  1. ∠ABC = 180° - ∠AEC   [ Opposite angels of cyclic quadrilateral are supplementary.]
  2. Since ∠ABC = ∠ADE   [ Opposite angles of parallelogram are equal.]
    ∠ADE = 180° - ∠AEC
  3. ∠ADE = ∠AED   [ 180° - ∠AEC = ∠AED]
  4. Since ADE is isosceles with angles ∠ADE = ∠AED, AD = AE, therefore  
    AE
    AD
      = 1.

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