First slide

Definition of a circle

Question

$A, B, C$ and D are the points of intersection with the coordinate axes of the lines
$a x + b y = a b$ and $b x + a y = a b$ then ,

Moderate

A

$A, B, C, D$ are concyclic
B

$A, B, C, D$ form a parallelogram
C

$A, B, C, D$ form a rhombus
D

none of these

Solution

The coordinates of A, B, C and D are A (b, 0), B (0, a), C (n, 0), D (0, b) respectively.
Clearly , $O A \cdot O C = O B \cdot O D = a b$
So, $A, B, C, D$ are concyclic points.

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