Question

ABC is 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

Answer 1

Answer:

Step-by-step explanation:

Draw line AD and DC such that

and

.

and

ABCD is a rectangle as it has opposite sides equal and parallel.

All angles of rectangle are

and rectangle has two diagonals equal and bisect each other.

Hence, AO = BO = CO = DO

O is equidistant from A,B,C,D.

Answer 2

Draw lines AD and DC such that AD||BC,

AB||DC

AD = BC, AB = DC

ABCD is a rectangle as opposite sides are equal

and parallel to each other and all the interior angles are of 90°.

In a rectangle, diagonals are of equal length and also these bisect each other.

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B, and C.