Q. 105.0( 2 Votes )

Prove that the lengths of two tangents drawn from an external point to a circle are equal.


Answer :

Let us consider a circle with center O.


TP and TQ are two tangents from point T to the circle.


To Proof : PT = QT


Proof :


OP PT and OQ QT


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


OPT = OQT = 90°


In TOP and QOT


OPT = OQT


[Both 90°]


OP = OQ


[Common]


OT = OT


[Radii of same circle]


TOP QOT


[By Right Angle - Hypotenuse - Side criterion]


PT = QT


[Corresponding parts of congruent triangles are congruent]


Hence Proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on Circles37 mins
Short Cut Trick to Find Area of Triangle43 mins
Quiz | Area Related with Circles47 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
view all courses