Question

Construct a tangent to a circle at a given point when the centre of the circle is known.

Answer 1

Steps of construction:

Step 1: Draw a circle with a certain radius and mark the centre as point O. Also, consider a point, which lies on the same circle and name it as P. Join OP.

Step 2: Through the point P, draw a perpendicular line and name it as XY.

Step 3: In our construction, XY is the required tangent to the given circle passing through P.



Let’s verify our construction.

Since the line XY passes through the point P of the circle and it is perpendicular to radius as per our construction.
We know that, the tangent at any point of a circle is perpendicular to the radius through the point of contact.
So, XY is a tangent passing through the point P for the given circle.