Q1 of 62 Page 10

Is the length of tangent from an external point P on a circle with center 0 is always less than OP?

Consider a figure for the problem in which we have a circle with center O.

PT is a tangent drawn from external point P. Joint OT.


OT ⏊ PT [ As tangent at any point on the circle is perpendicular to the radius through point of contact]



So, OPT is a right-angled triangle formed.


In right angled triangle, hypotenuse is always greater than any of the two sides of the triangle.


So,


OP > PT or PT < OP


Hence, Length of tangent from an external point P on a circle with center O is always less than OP.


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