Question

In a quadrilateral ABCD, there is a point O inside it such that OB =OD Also, AB = AD and BC =DC prove that O lies on AC. ​

Answer 1

Step-by-step explanation:

AB = AD  =>  ΔABD is isosceles

=>  A is on the perpendicular bisector of BD

BC = DC  =>  ΔCBD is isosceles

=>  C is on the perpendicular bisector of BD

OB = OD  =>  ΔOBD is isosceles

=>  O is on the perpendicular bisector of BD

So points A, C, O all lie on the same line (the line AC).

That is, O lies on AC.