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Consider the following statements about a right-angled triangle: Statement-1: For any right-angled triangle, the value of \((a^2+b^2+c^2)/R^2\) is always 8. Statement-2: \(a^2=b^2+c^2\). Choose the correct option.

1. Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1
2. Statement-1 is true, Statement-2 is true; Statement-2 does not correctly explain Statement-1
3. Statement-1 is false, Statement-2 is true
4. Statement-1 is true, Statement-2 is false

Correct answer: Statement-1 is true, Statement-2 is false

Solution

Statement-1 is true because it correctly describes the relationship between the sides of a right-angled triangle and its circumradius, while Statement-2 is false as it misrepresents the Pythagorean theorem, which states that the square of the hypotenuse equals the sum of the squares of the other two sides.

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