Prove that the tangent at any point of a circle is perpendicular to theradius through the point of contact.

Solution

$Given : A circle with centre O and a tangent XY to the circle at a point P To prove : OP is perpendicular to XY . Construction : Take a point Q on XY other than P and join OQ .$

$Proof : Here the point Q must lie outside the circle as if it lies inside the tangent XY will become secant to the circle . Therefore, OQ is longer thanthe radius OP of the circle, That is, OQ > OP . This happens for every point on the line XY expect the point P . So OP is the shortest of all the distance of the point O to the points on XY . And hence OP is perpendicular to XY . Hence, proved .$

For Daily Free Study Material Join wiredfaculty

Circles

Prove that the tangent at any point of a circle is perpendicular to theradius through the point of contact.

Some More Questions From Circles Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction