Question

Statement (1): O and O' are centres of two equal circles and ABCD is a straight line.

Statement (2): If OР ⊥ АВ, O'Q ⊥ CD and O'Q is greater than OP, then CD > AB.

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

Statement 1 is true, and statement 2 is false.

Explanation:

• Statement (1): The diagram depicts two equal circles with centres O and O' intersected by a straight line forming chords AB and CD in each circle respectively, making Statement (1) true.
• Statement (2): In equal circles, chords that are closer to the centre are longer. If O'Q is greater than OP, it means chord CD is located further away from the centre than chord AB. Therefore, chord CD should be shorter than chord AB (CD < AB), not greater. This makes the claim that CD > AB false.