Consider the following statements:<br>1. The angle in a sector greater than a semi-circle is less than a right angle.<br>2. If two sides of a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.<br>Which of the statements given above is/are <strong>CORRECT</strong>?
- A. 1 only
- B. 2 only
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Statement 1 is correct because the angle subtended by a minor arc in the major segment is acute (less than 90^\circ). Statement 2 is correct because a cyclic quadrilateral with one pair of equal opposite sides forms an isosceles trapezium, in which the diagonals are of equal length.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...