Question

the number of incorrect statements is ______. ①the major arc must be longer than the minor arc; ②two circles with the same area are congruent circles; ③the arcs with the same length are congruent arcs; ④through a point inside the circle, we can draw infinite chords. ⑤through a point inside the circle, we can draw infinite diameters. a. 1 b. 2 c. 3 d. 4

Explanation:

Step1: Analyze statement ①

By definition, a major arc is longer than a minor arc, so this statement is correct.

Step2: Analyze statement ②

If two circles have the same area, since the area formula of a circle is $A = \pi r^{2}$, they have the same radius and are congruent circles, so this statement is correct.

Step3: Analyze statement ③

Arcs with the same length in different - sized circles are not congruent. Congruent arcs must be in the same circle or congruent circles and have the same length and measure. So this statement is incorrect.

Step4: Analyze statement ④

Through a point inside a circle, we can draw infinite chords. A chord is a line - segment joining two points on the circle, and we can connect the interior point to different pairs of points on the circle, so this statement is correct.

Step5: Analyze statement ⑤

A diameter is a chord passing through the center of the circle. Through a non - center point inside the circle, we can draw only one diameter (if the point is the center, there are infinite diameters). So this statement is incorrect.

Answer:

C. 3