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).

Solution:

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles measure 90°.

Thus, AD ∥ BC, AB ∥ DC and AD = BC, AB = DC

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

Hence, AO = OC = BO = OD

Thus, two right triangles make a rectangle where O is an equidistant point from A, B, C, and D because O is the mid-point of the two diagonals of the rectangle ABCD.

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

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4 Question 6

Summary:

ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. O is the equidistant point from A, B, C, and D because O is the mid-point of the two diagonals of the rectangle ABCD.

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