In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, prove that arc AD = arc CB.
Hint: Minor arc AB = minor arc CD. Subtract minor arc BD from both sides.

Given AB=CD
Now subtract BD from both sides
If equals are substracted from equals the wholes are equal(euclids axiom)
  • 1
As it is given in the question that chord AB = chord CD
So, arc AB should also be equal to arc CD because if two chords of a circle are equal the their corresponding arcs are also congruent.
arc AB = arc CD
Now, we can subtract arc BD from the above equation as it is common
arc AB - arc BD = arc CD - arc BD
arc AD = arc CB

  • 3
What are you looking for?