2022 · Q61
Consider the following statements :
- 1If two chords AB and AC of a circle are equal, then the centre of the circle lies on the angle bisector of angle CAB.
- 2If two concentric circles are intersected by a line at A, B, C and D respectively, then AC = BD.
Which of the above statements is/are correct?
Elementary MathematicsCircles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Equal chords AB = AC from A are mirror images across the line through A and the centre, which therefore bisects ∠CAB - statement 1 is true. For concentric circles, the perpendicular from the common centre bisects both chords, making the outer segments equal - statement 2 is true. Hence the keyed option is C.