Ritika Das
Last Activity: 7 Years ago
Suppose a circle has a centre O with T on the boundary of the circle from where the tangent has been formed. Let P be the foot of the radius drawn from centre O of the circle. Suppose T and P to be different points at first.
Now, since OT is greater than OP, and angle OPT is equal to 90 degrees, therefore angle OTP is greater than angle OPT.
So angle OTP is greater than 90 degrees.
Contradictingly, the angle sum of triangle OPT is seen to be greater than 180 degrees, while violates the angle sum property of a triangle. So we conclude that T and P are the same point, and moreover the tangent creates a 90 degrees angle along with the radius perpendicular on it.