Question

AB lies in the same plane as circle P, which has a radius of 6 mm. At how many points will AB intersect circle P if PA is 7mm and PB is 3mm?

Answer 1

Answer:

At one point AB will intersect circle P.

Step-by-step explanation:

Given information: Radius of circle P is 6 mm, PA=7 mm  and PB= 3 mm.

The length of PA is 7 mm which is more than the radius of circle P. So, we can say that the point A lies out side the circle.

The length of PB is 3 mm which is less than the radius of circle P. So, we can say that the point B lies inside the circle.

If a point lies outside the circle and one point lies inside the circle , then the line segment joining these two points intersect the circle at one point.

Since the point A lies outside the circle and point B lies inside the circle , therefore the line segment AB intersect the circle at one point.

Answer 2

PA is longer than the radius of the circle so Point A must be outside of the circle.

PB is less than the radius of the circle so Point B must be inside the circle.

Since the ray is going from A to B it is coming inside the circle and continuing in the other direction, therefore, it must exit the circle, giving us 2 contact points