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 . -Maths 9th

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 . -Maths 9th
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Answer :

Given radius =2​cm Therefore AO=2​cm Let OD be the perpendicular from O on AB  And AB =2cm Therefore AD=1cm        (perpendicular from the centre bisects the chord) Now in triangle AOD, AO=2​cm AD=1cm And let angle AOD =θ Therefore , sinθ=2​1​Hence, θ=45o Therefore angle AOB =45o+45o=90o Then angle APB =290​=45o            {angle made by a chord at the centre is double of the angle made by the chord at any poin on the circumference)
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