Question

ramya said the length of a tangent of a circle with center o from a point p which is out side of the circle is always less than op .Do you agree give reason​

Answer 1

Answer:

Step-by-step explanation:

Let the tangent touches the circle at Q it is the point of contact and perpendicular to the radius triangle POQ angle M =90° OP = hypotenuse we know that hypotenuse is the longest side in right angle triangle so .˙. Length of the tangent will always be less than OP

Answer 2

True, length of a tangent of a circle with center o from a point p which is out side of the circle is always less than OP

Step-by-step explanation:

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 .

#Learn more:

Prove that the tangent to a circle is perpendicular to the radius of the circle

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