Question

Assertion (A): Angle BOC = 90°.

Reason (R): OC² = 3² + 4² = 25, OB² = 6² + 8² = 100, OC² + OB² = 125 = BC².

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, and R is the incorrect reason for A.

Answer 1

Both A and R are true, and R is the incorrect reason for A.

Explanation:

• Assertion (A): In ΔOBC, the side lengths are OC = 5 cm, OB = 10 cm, and BC = `5sqrt{5}` cm. Since OC² + OB = 5² + 10² = 25 + 100 = 125 and `BC^2 = (5sqrt{5})^2` = 125, the converse of Pythagoras’ theorem confirms that ΔOBC is a right-angled triangle with ∠BOC = 90°.
• Reason (R): The reason explicitly calculates OC² = 3² + 4² = 25 and OB² = 6² + 8² = 100, demonstrating that their sum equals BC² (125), which directly provides the mathematical proof and logical basis for Assertion (A).