Question

The radius of a circle is $16cm$. The mid point of a chord of the circle lies on the diameter perpendicular to the chord and its distance from the near end of the diameter is $3cm$; If the length of that chord is $m\sqrt{87}$ cm, then the value of $m$ is

• A. $4$
• B. $8$
• C. $2$
• D. $1$

Answer 1

Answer: (C)

$2$

Radius of circle $=16cm$

Length of perpendicular to chord from center $=16-3=13cm$

Perpendicular from center to any chord bisects the chord.

So, by Pythagoras' theorem, the half length of the chord is $=\sqrt{{16}^2-{13}^2}=\sqrt{87}$

So the length of the chord is $=2\sqrt{87}cm$

So option C is the right answer.