Question

abc is right angle ttaingle and o is the mid point of the side oppsite to the right angle. explain why o is the equistant from a, b and c​

Answer 1

Answer:

Step-by-step explanation:

Between Δ AOD & Δ BOC we have  AO=CO (given),BO=OD (by Construction).

∠ AOD   =∠ BOC....Vertically opposite angle

∴  By SAS test Δ AOD &  Δ BOC are congruent.

So AD=BC....(i)

similarly, between Δ AOB &  Δ DOC we have  AO=CO (given), BO=OD (by Construction)

∠ AOB   =∠ DOC

∴  By SAS test Δ AOB &  Δ DOC are congruent.

So AB=DC.....(ii)

Also ∠ ABC=90  

o

....(iii)

∴  From (i) &  (ii) &  (iii) we conclude that ABCD is a rectangle.

So the diagonals AC &  BD are equal and bisect each other at O.

∴  OA=OB=OC=OD.

i.e O is equidistant from A, B &  C.