Question

Assertion :In any right angled triangle $\frac{a^2+b^2+c^2}{R^2}$ is always equal to $8$. Reason: $a^2=b^2+c^2$ or $b^2=c^2+a^2$ or $c^2=a^2+b^2$

• 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. Both Assertion and Reason are incorrect

Answer 1

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

Reason: is true (from Pythagoras theorem)

Assertion: Let $\angle A=\frac{\pi }{2}\Rightarrow a^2=b^2+c^2$

$\therefore \frac{a^2+b^2+c^2}{R^2}=\frac{2a^2}{R^2}=2{\left[\frac{a}{R}\right]}^2=2{\left(2\sin A\right)}^2$

$=2\left[4{\sin }^2\frac{\pi }{2}\right]=8$

Hence assertion and reason both are true and reason correctly explains assertion.