Question

Assertion :Statement-1: If $a$ is a constant and two chords of length $a^2-1$ and $3(a+1)$ of a circle bisect each other, the radius of the circle is $\frac{15}{2}$. Reason: Two chords of a circle bisect each other only when both are the diameters of the circle.

• 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

Statement-$2$ is true because centre of the circle is the only point, such that all chords passing through it are bisected by it.

Using this result in statement-1, as both the chords are diameters
$\Rightarrow a^2-1=-3(a+1)$
$\Rightarrow a^2-3a-4=0\Rightarrow a=4$ or $-1$

But, $a\ne -1$ ...(Length cannot be negative)

So, $a=4$ and the radius of the circle is

$=\frac{3(a+1)}{2}=\frac{15}{2}$

and thus statement-$1$ is also true.