Largest distance of an external point from a circle

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Largest distance of an external point from a circle

Let us consider a point and a circle as shown in the below figure.


Let us draw a line segment as shown in the below figure.

Now let us draw a circle with the length of PQ as radius as shown in the below figure.


Therefore, here length of line segment PQ is equal to the radius of the bigger circle.

We can find the distance of the point from the circle along different line segments as shown in below figure.

We know that , the length of line segment PQ is equal to the radius of the bigger circle.

If we observe the above figure, the lengths of line segments joining the point ‘p’ and the points on the circle other than the line segment PQ , are less than the radius of the bigger circle.

Therefore, the length of line segment PQ is the greatest among the lengths of all other line segments joining the points on the circle and the considered point as the length of line segment PQ is equal to radius of the bigger circle and the lengths of all other line segments joining the points on the circle and the considered point are less than the radius of the bigger circle.

Therefore from above observation, the greatest distance of a point from a circle is equal to the distance of the point from circle along the line segment joining the point and the centre of the circle.


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