a circle has radius root 2 cm. It is divided into 2 segments by a chord of length 2cm. proved that angle subtended by the chord at the point in measure segment is 45 degree

Given that: radius of circle OQ = OR =  cm

And length of chord (QR) = 2 cm

In,

  is a right-angled triangle, So,

Since, Angle at the centre is double the angle on the remaining part of the circle.

Hence, angle subtended by the chord at the point in major segment is 45 degree.

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GIVEN AO = BO = √2 cm and , AB = 2 cm
TO PROVE y = 450
SOLUTION in triangle AOB , AO2+BO2 = AB2
 
(√2)2+(√2)2 = (2)2
so , x = 900 (by Converse of Pythagoras Theroem)

y = x/2 (angle subtended by a chord at any point in the alternate segment is half than that subtended at the centre)
hence , y = 90/2 = 450...


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