Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre?

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asked Mar 13, 2018 in Mathematics by paayal (26,720 points) 4 6 11
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre?

1 Answer

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answered Mar 13, 2018 by sanjaydas (61,430 points) 5 7 7
selected Mar 14, 2018 by faiz
 
Best answer

Solution: In the given figure, QR is diameter and O is
centre. OP, SP and RP are lines touching the tangent at
the point of contact.
In triangles POS and POR
Line PS > PO and SO
Line PR > PO and RO
So, PS and PR are hypotenuses of respective triangles.
So, it is proved that Angle POR = Right Angle
If PO is increased to reach the other end of the perimeter, then it will be the diameter.

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