"There is no chord of a circle that is longer than its diameter." How do you justify this statement? Class 9
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"There is no chord of a circle that is longer than its diameter." How do you justify this statement? Class 9
Question 1.
"There is no chord of a circle that is longer than its diameter." How do you justify this statement? Class 9
Solution:
Consider a circle with centre O and radius r.
Let AB be any chord of the circle.
OA = OB = r
Now, in any triangle,
Sum of any two sides > third side
∴ OA + OB > AB
∴ r + r > AB
∴ 2r > AB
But 2r is the diameter of the circle.
∴ No chord is longer than the diameter.