A circle has radius √2 cm. It is divided into two segments by a chord of length 2cm.Prove that the angle subtended by the chord at a point in major segment is 45 degree .

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asked Sep 27, 2018 in Class IX Maths by navnit40 (-4,746 points)

A circle has radius √2 cm. It is divided into two segments by a chord of length  2cm.Prove that the angle subtended by the chord at a point in major segment is 45.

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answered Sep 27, 2018 by muskan15 (-3,437 points)

Solution  :-

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

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