Question

ABC is a right-angled triangle and O is the mid point of the side
opposite to the right angle. Explain why O is equidistant from A,
B and C. (The dotted lines are drawn additionally to help you).​

Answer 1

Answer:

ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B, and C. (The dotted lines are drawn additionally to help you).

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ANSWER

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.