If the points `(a, 0), (b,0), (0, c)`, and `(0, d)` are concyclic `(a, b, c, d > 0)`, then prove that `ab = cd`.

Explanation

Without loss of generality, assume that `bgtaanddgtc`. SinceABCD is cyclic quadrilateral, sum of oppsite angles is `180^@`.

i.e., `angle BAC+ angle CDB=180^@`
Let ` angleBAC=theta` (=inclination of line AC)
`therefore angle CDB=180^@-theta`
Therefore, inclination of line BD is `270^@-theta` slope of line AC.
`tantheta=-(c)/(a)`
Slope of `BD, tan (270^@-theta)=-(d)/(b)`
or `cot theta=-(d)/(b)`
From (1) and (2), we get
`(tantheta)(cottheta)=(-(c)/(a))(-(d)/(b))`
or `ab=cd`