Question

Statement 1: A tangent is perpendicular to the radius at the point of contact.
Statement 2: A line from the centre to any other point on the tangent has a length greater than the radius of the circle.

• A. Statement 1 is the correct explanation for statement 2.
• B. Statement 2 is the correct explanation for Statement 1
• C. Statement 1 and Statement 2 are false.
• D. Statement 2 is a theorem and Statement 1 is false.

Answer 1

The correct option is B Statement 2 is the correct explanation for Statement 1

A tangent is perpendicular to the radius at the point of contact. This is a theorem.

Here, P is the point of contact of the tangent. P’ is any other point on the tangent.
Now OP’ > OP
Hence, OP is the shortest distance of the tangent from the centre. OP is also the radius
And we know that the shortest distance of a point from the centre will be the perpendicular distance.

Thus, OP is perpendicular to the tangent.