How many tangents to the circle can be constructed through point P?

There can be 3 possibilities to this problem, depending upon the location of the point.

Answer: Depending upon the location of point P, 0, 1 or 2 tangents are possible from a single point to the circle.

A point can be located internally, externally or even on the circumference of the circle.

Explanation:

There are three different cases possible, which are discussed below, one by one.

Case 1) When point P lies inside the circle.

In such cases 0 tangents are formed since the line drawn through them, will form a secant, and not a tangent.

Case 2) When the point p lies on the circumference of the circle.

1 tangent can be drawn from it since the perpendicular drawn from it is neither less than nor greater than the radius of the circle, but exactly equal to it.

Case 3) When the point p lies outside the circle.

2 tangents are possible since the perpendicular distance of the point from the circle's center is greater than the radius of the circle.

Thus, depending upon the location of point P, 0, 1, or 2 tangents are possible from a single point to the circle.