Consider the following statements :<br><br>1. In an equilateral triangle, the centroid and centre of circumcircle coincide.<br>2. Angle bisectors of a cyclic quadrilateral form another cyclic quadrilateral.<br>3. Every cyclic parallelogram is a rectangle.<br><br>Which of the statements given above are <strong>CORRECT</strong>?
- A. Only 1 and 2
- B. Only 2 and 3
- C. Only 1 and 3
- D. 1, 2 and 3 ✓
Correct Answer: D. 1, 2 and 3
Explanation
All three standard geometry theorems apply: 1) Centers naturally coincide in an equilateral triangle. 2) The intersection of internal angle bisectors of any cyclic quadrilateral forms a cyclic quadrilateral. 3) Opposite angles in a parallelogram are equal; for a cyclic parallelogram, their sum is 180^\circ, making each 90^\circ (a rectangle).
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