Question

which of the following statements are true and which are false? if the statement is
(a)two circles can intersect at exactly one point.
(b)two circles can intersect at exactly two points.
(c)two circles can intersect in no points.
(d)two circles can intersect in exactly three points.
(e)two circles can intersect in four or more points.

(a) choose the correct answer below.
the statement is true.
the statement is false
(b) choose the correct answer below
the statement is true
the statement is false

Explanation:

(a) Two circles can be tangent (touch at exactly one point), so this is true.
(b) Two distinct non-tangent circles can cross each other at two distinct points, so this is true.
(c) Two circles can be separate (one entirely inside the other without touching, or both outside and not touching) so they have no intersection points, so this is true.
(d) Two distinct circles cannot intersect at three points; if three points are common, the circles are identical, so this is false.
(e) Two distinct circles cannot share four or more points; this would mean they are the same circle, so this is false.

Answer:

(a) The statement is true.
(b) The statement is true.
(c) The statement is true.
(d) The statement is false.
(e) The statement is false.