Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

ABCD is a cyclic quadrilateral

ABCD is a cyclic quadrilateral,  with side
AD= d
where d is the diameter of the circle. AB= a

BC= a
and CD= b
If a, b and d are integers a ≠ b

(a)prove that d cannot be a prime number
         .

(b)determine the minimum value of d.

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: ABCD is a cyclic quadrilateral

let O be the center of circle
join AC and OB let they meet at  E.
Now triangle ABO and triangle BCO are congruent. and it can be proved that AC and BO are perpendicular.
Now

area of triangle ABO can be calculated in two ways i.e

............1

.................2

equaling (1) and (2) and simplifing

which shows that d has the factors both not equal to 1 or zero.
hence d cant be prime.
  for minimum value i am trying

Last edited by gyanshrestha (2007-11-22 22:40:22)

---

http://gyan.talkacademy.com.np