Given: A chord AB of length 2cm and radius of the circle is √2cm
To prove: ∠ACB = 450
Proof: In △AOB,
OA2 + OB2 = (√2)2 + (√2)2 = 2 + 2 = 4 = AB2
⇒ △AOB is a right triangle right angled at O.
i.e. ∠AOB = 900
As the angle subtended by an arc at the centre is double the angle subtended by it at remaining part of the circle.
∴ ∠AOB = 2∠ACB
⇒ ∠ACB = 1/2 x 900 = 450