Question

In a circle of radius 13 𝑐𝑚, two chords $MN$ and $JK$ are at a distance of 5 𝑐𝑚 from the centre. Find the measure of $(MN+2\times JK)$ .

Answer 1

Let $OP$ be the perpendicular drawn from the centre of the circle to the chord $MN$.
The perpendicular drawn from the centre of the circle to the chord bisects the chord.
$\therefore MP=PN$

We know that, equal chords are equidistant from the centre of the circle, and vice versa.
Here, $OP=OQ=5cm$ (given)
According to the theorem, we get
$MN=JK$
$OM=13cm$ (radius of the circle)

Consider $△OPM$
Applying Pythagoras theorem,
$O{M}^2=O{P}^2+M{P}^2$
${13}^2=5^2+M{P}^2$
$M{P}^2=169-25=144$
$\therefore MP=12$

As $MP=PN=12cm$
$\therefore MN=24cm$
As $MN=JK=24cm$
$\therefore MN+2\times JK=(24+48)cm=72cm$

Answer: $MN+2\times JK=72cm$