Question

prove that the rectangle circumbrising a circle is a square
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Answer 1

Answer:

In the provided figure the marking are done by the rule that 'the two tangents drawn to a circle from a fixed point has same length'

As the quadrilateral is a rectangle

       a+d=b+c

   ∴ a=b+c-d-----------------------------------(1)

From the above reason

      a+b=c+d

   from (1)

       b+c-d+b=c+d

   ⇒ 2b=2d

   ⇒ b=d-----------------------------------------(2)

Substituting from (2) in (1)

       a+d=c+d

   ⇒ a=c------------------------------------------(3)

  

   From (2) and (3)

      a+d = a+b-----------------------------------(4)

  Similarly we can prove that

      a+b=b+c-----------------------------------(5)

and      b+c=c+d------------------------------------(6)

and      c+d=a+d------------------------------------(7)

From (4) , (5) , (6) and (7) we can prove that the rectangle is a square.