Consider the following statements :<br>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.<br>2. If two concentric circles are intersected by a line at A, B, C and D respectively, then AC=BD.<br>Which of the above statements is/are correct?

Explanation

Statement 1 is a known property: equal chords subtend equal angles at the center, and the line joining the center to the intersection of the chords bisects the angle between them. Statement 2 is also correct: a perpendicular from the center bisects both chords, so if M is the midpoint, AM=MD and BM=MC. Subtracting them gives AB=CD, adding BC gives AC=BD.

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