point O is the centre of the circle lines x and y are parallel tangents to the circle at A and B respectively prove that segment AB is a diameter of the circle
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Given :
Line a & b are tangents to the circle with Centre 'O' touching at points P & Q respectively. Also tangent a || b.
To prove :
Seg PQ is a diameter.
Solution :. In circle with Centre 'O',
By tangent theorem,
Tangent a is perpendicular to Seg OP
& tangent b is perpendicular to Seg OQ
Therefore, angle OPT=angle OQR=90°
Tangent a || Tangent b
& Seg PQ is the transversal
Also P-O-Q as it passes through the Centre
Therefore, seg PQ is the diameter to the given circle.
Hence, proved!
Line a & b are tangents to the circle with Centre 'O' touching at points P & Q respectively. Also tangent a || b.
To prove :
Seg PQ is a diameter.
Solution :. In circle with Centre 'O',
By tangent theorem,
Tangent a is perpendicular to Seg OP
& tangent b is perpendicular to Seg OQ
Therefore, angle OPT=angle OQR=90°
Tangent a || Tangent b
& Seg PQ is the transversal
Also P-O-Q as it passes through the Centre
Therefore, seg PQ is the diameter to the given circle.
Hence, proved!
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