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?
The AB intersects circle P if PA is 7mm and PB is 3mm it must exit the circle, and it has 2 contact points.
PA is longer than the radius of the circle so Point A must be outside of the circle.
We have given that,
AB lies in the same plane as circle P, which has a radius of 6 mm.
Two or more circles intersect at one point. Two circles can be tangent to each other in two different ways
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.
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