Question

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

• A. Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1
• B. Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1
• C. Statement-1 is true, Statement-2 is false
• D. Statement-1 is false, Statement-2 is true

Answer 1

The correct option is A Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1

Both chords are diameters $\Rightarrow a^2-1=3(a+1)$
$\Rightarrow$ a = 4 or -1
a = -1 is not possible
$\therefore a=4$
Radius of circle $\frac{3(a+1)}{2}=\frac{15}{2}$