Question

The points $A(a,0),B(0,b),C(c,0)$ & $D(0,d)$ are such that $ac=bd$ & a, b, c, d are all non-zero. Then the points.

• A. Form a parallelogram
• B. Do not lie on a circle
• C. Form a trapezium
• D. Are concyclic

Answer 1

The correct option is D Are concyclic

The points $A(a,0),B(0,b),C(c,0)$ and $D(0,d)$ are such that $ac=bd$ and $a,b,c,d$ are all non-zero.

$ac=bd$ [ Given ]

$\Rightarrow$ $AO\times OC=OB\times OD$

This is true in case of circle and two secants.

$\therefore$ $A,B,C$ and $D$ lie on a circle.

$\therefore$ The given points are concyclic.