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×JK).

Answer 1

Construction:

Construct the diagram with the help of the given information.

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.

∴ MP = PN

• We know that equal chords are equidistant from the centre of the circle, and vice versa.

Here, OP = OQ = 5 cm (given)

According to the theorem, we get

MN = JK

• OM = 13 cm (radius of the circle)

• Consider triangle OPM.

<Write and dictate:

Applying Pythagoras theorem,

$O{M}^2=O{P}^2+M{P}^2$

${13}^2=5^2+M{P}^2$

$M{P}^2=169-25=144$

MP = 12

∴ MP = PN = 12 cm

MN = 24 cm

∴ MN = JK = 24 cm

MN + 2×JK = (24 + 48) cm = 72 cm

Hence , MN + 2×JK = 72 cm