Question

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

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

Answer 1

The correct option is A Both Assertion and Reason are individually true and Reason is the correct explanation of Assertion.

$a^2=b^2+c^2,$ then $\angle A=\frac{\pi }{2}$ by Pythagoras theorem
$\therefore a=2R\sin A$ using sine rule
$\Rightarrow a=2R\sin \frac{\pi }{2}=2R$ since $\sin \frac{\pi }{2}=1$
$\Rightarrow \frac{a^2+b^2+c^2}{R^2}$
$=\frac{a^2+a^2}{R^2}$ since $b^2+c^2=a^2$ (given)
$=\frac{2a^2}{R^2}$
$=\frac{2{\left(2R\right)}^2}{R^2}$ since $a=2R$ as above.
$=8$