Question

A point Of is taken inside a quadrilateral ABCD such that it's distances from the angular points D and B are equal. Show that OA and OC are in one and same straight line.

Answer 1

Question is like this
a point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. show that AO and OC are in one and the same stright line

Given : A point O is taken inside an equilateral quadrilateral ABCD such that DO = BO

To prove: AO and CO are in one and the same straight line

Proof: In

AD = AB (Given equilateral quadrilateral)

AO = AO (common)

OD = OB (Given)

Hence,

Therefore , angle AOD = angle AOB ……………..(1)

Similarly ,

Angle CDO = angle BOC ……………...(2)

But, angle AOD + angle AOB + Angle CDO + angle BOC = 360

2 angle AOB + 2 angle BOC = 360 (From eqn (1) and (2) )

2 (angle AOB + angle BOC )= 360

angle AOB + angle BOC = 180

Hence their outer arms AO and OC are in same and straight line

Hence proved

Figure cant be drawn
so please draw fig and lokk through this