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State True or False. In a circle if a chord of length $$\sqrt{2}$$ subtends an angle of $$45^\circ$$ at a point on the circumference of the circle then the radius of the circle is 1.
Correct Answer: True
The angle at the centre is twice the angle at the circumference, so the chord subtends $$90^\circ$$ at the centre. Then the chord is $$r\sqrt{2}$$, and $$r\sqrt{2} = \sqrt{2}$$ gives $$r = 1$$. The statement is True.
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