Question

Line AB lies in the same plane as circle p, which has a radius of 6 mm. At how many points can AB intersect circle p if AP = 7 mm and BP = 3 mm?

A. 2
B. 1
C. 0
D. There is not enough information to determine.

Answer 1

I think the answer is B? They didn't say whether point P is in the centre of the circle, so the answer could also actually be D. But assuming that P is the centre point of the circle, the answer should be B.

AP (7mm) > Radius of circle p (6mm)
meaning that the line should extend out of the circle from the centre of it and thus produce one intersection.

As for the rest of the line, BP,
BP (3mm) < Radius of circle p (6mm)
meaning that if the distance of point P to point B is shorter than the distance of point p from the line of the circle (this distance being the radius), it should not make another intersection.

Therefore, there is only 1 intersection and the answer should be B (if point P is the middle of circle p)

Answer 2

A

Explanation:

just got the answer