Which of the following is a correct statement?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. If two circles touch each other, the point of contact lies on the line joining the two centres.
(a) The sum of the angles of a cyclic quadrilateral is always 180°. = This statement is incorrect. The sum of the opposite angles of a cyclic quadrilateral is 180°, but the sum of all the angles is 360°.
(b) Equal chords are equidistant from the centre of the circle but not always subtend equal angles at the centre of the circle. = This statement is incorrect. Equal chords are equidistant from the center, and they also subtend equal angles at the centre of the circle.
(c) If two circles touch each other, the point of contact lies on the line joining the two centres. = This statement is correct. When two circles touch each other (either externally or internally), the point of contact lies on the line joining their centres.
(d) Angles subtended by the arc in the same segment of the circle are in the ratio of 2:1. = This statement is incorrect. Angles subtended by the same arc in the same segment of a circle are equal.