If AOB is the diameter of a circle and C is a point on the circle, then AC² + BC² = AB². Is the given statement true or false and justify your answer

Solution:

We know that

A diameter of a circle subtends a right angle to any point on the circle

If AOB is the diameter and C is a point on the circle

Triangle ACB is right angled at C

In triangle ACB

Using the Pythagoras theorem

AC² + BC² = AB²

Therefore, the statement is true.

✦ Try This: If POQ is a diameter of a circle and R is a point on the circle, then PR² + QR² = PQ².

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 6

If AOB is the diameter of a circle and C is a point on the circle, then AC² + BC² = AB². Is the given statement true or false and justify your answer

Summary:

The statement “If AOB is a diameter of a circle and C is a point on the circle, then AC² + BC² = AB²” is true

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