Question

Assertion :In a right angle $\Delta ,\frac{a^2+b^2+c^2}{R}$ is always equal to $8$. Reason: $b^2=a^2+c^2$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion false but Reason is true

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

According to $a^2+c^2=b^2$

$\angle B={90}^o$

Therefore, According to sine Rule

$\frac{b}{sinB}=2R\Rightarrow b=2R\ast sin{90}^o=2R$

Now, $\frac{b^2+(a^2+c^2)}{R^2}=$ $\frac{2b^2}{R^2}=\frac{2\ast 4R^2}{R^2}=8$

Therefore, Reason is Correct Explaination of Assertion