Question

The radius of a circle is 13cm. Length of one of its chord is 24cm. Find distance of chord from the centre

Answer 1

   

The perpendicular distance of a chord from the center of the circle is the square root of sum of squares of half the chord and the radius.

If r is the radius of the circle and a is the length of the chord, then the distance of the chord from the center is √(r²+(a/2)²).

Here,

$\Rightarrow\ \sqrt{13^2-(24/2)^2} \\ \\ \Rightarrow\ \sqrt{13^2-12^2} \\ \\ \Rightarrow\ \sqrt{169-144} \\ \\ \Rightarrow\ \sqrt{25} \\ \\ \Rightarrow\ \bold{\mathfrak{5\ cm}}$

So the distance of the chord frm the center of the circle is 5 cm.

Plz ask me if you have any doubt on my answer.

$\boxed{\textit{Thank you...}}$

$\mathfrak{\#adithyasajeevan}$

Answer 2

Answer:

Let PQ be a chord of a circle with centre O and radius 13cm such that PQ = 24cm.

From O, draw OM perpendicular PQ and join OP.

As, the perpendicular from the centre of a circle to a chord bisects the chord.

∴  PM = 12cm

In △OMP, we have

OP2 = OM2 + PM2

⇒ 132 = OM2 + 122

⇒ OM = 5cm.                                                                                                                                                      Hence, the distance of the chord from the centre is 5cm.

Step-by-step explanation: