Multiple choice

Consider the following statements: 1. If two chords AB and AC of a circle are equal, then the centre of the circle lies on the angle bisector of angle CAB. 2. If 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?

  1. 1 only

  2. 2 only

  3. Both 1 and 2

  4. Neither 1 nor 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement 1 is a standard geometry theorem: the locus of points equidistant from two lines is the angle bisector. Statement 2 is also a standard theorem: a line intersecting concentric circles creates chords of equal length between the outer and inner circles, so AC = BD.

AI explanation

In statement 1, equal chords AB and AC subtend equal angles at the centre, making the centre equidistant from sides AB and AC, which proves it must lie on the angle bisector of angle CAB. In statement 2, a perpendicular from the common centre to the intersecting line bisects the chord of the larger circle (AD) and the chord of the smaller circle (BC), meaning the distances from that midpoint to the ends are equal, verifying AC = BD. Both statements correctly apply circle theorems. The result is both 1 and 2.

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