Question

Statement (1): In a circle with centre O, chord AB: chord BC = 1 : 3. If angle AOC is 160° ⇒ angle BOC = 120°.

Statement (2): AB : BC = 1 : 3 ⇒ ∠AOC = 3 × ∠AOB

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are false.

Explanation:

Statement 1 is false because central angles are proportional to arc lengths, not chord lengths. Furthermore, even if arc lengths were given, ∠AOC equals the sum of ∠AOB and ∠BOC (making it 4 times ∠AOB), which invalidates Statement 2.