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Is the following statement true or false?

The perpendicular at the point of contact of the tangent to a circle goes through the centre.

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True

False

answer is A.

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Detailed Solution

Given that the perpendicular at the point of contact of the tangent to a circle goes through the centre.
Question Image

We can see that

C

is a point on the line

EB

.
Length of

AC

is more than the length of

AF

which is the radius of the circle.

A C > A F

The difference is

FC

which is true for every other point lying on the line

BE

except

D

which is the shortest distance from line

EB

to center

A

, that is the radius

AD

. We know that the shortest distance between two points or lines is the perpendicular distance.

∴ A D ⊥ B E

Thus, the perpendicular at the point of contact of a tangent to the circle passes through the center of the circle.
Hence the given statement is true.
Therefore the correct option is 1.

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