Question

ABC is a right-angled triangle and O is mid-point of the side opposite to right angle. Prove that O is equidistant from A,B and C​

Answer 1

Answer:

PROVED

Step-by-step explanation:

CONSTRUCT: We produce A to D and join C and D to form a rectangle.

Between AOD and BOC we have AO=CO and BO=OD

Angle AOD= Angle BOC     [Vertically Opposite Angles]

Therefore By SAS congruence condition Triangle AOD and Triangle BOC are congruent. So AD=BC

Similarly, between triangle AOB and Triangle DOC are congruent

We have,

AO=CO and BO=OD

Angle AOB= Angle DOC

By SAS congruence condition Triangle AOB and Triangle DOC are congruent

So AB=DC

Angle ABC= 90 degree

We conclude that ABCD is a rectangle and AC and BD is a diagonal

AC=BD bisected by O

OA=OB=OC=0D

We prove that O is equidistant from A,B and C