Q. 324.3( 7 Votes )

Prove that the ta

Answer :



Given: A circle C (O, r) and a tangent AB at a point P.


We have to prove that OP AB.


Construction: Take any point Q, other than P on the tangent AB. Join OQ. Suppose OQ meets the circle at R.


Proof:


We know that among all line segments joining the point O to a point on AB, the shortest one is perpendicular to AB.


So, to prove that OP AB, it is sufficient to prove that OP is shorter than any other segment joining O to any point of AB.


OP = OR [Radii of the same circle]


Now, OQ = OR + RQ


OQ > OR


OQ > OP [ OP = OR]


OP is shorter than any other segment joining O to any point on AB.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
All GrammarAll GrammarAll Grammar41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses