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What will be the distance between two chords if they are on the same side of the centre in a circle of radius 5 cm, and their lengths are 8 cm and 6 cm respectively?

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1cm

2cm

4cm

3cm

answer is A.

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Detailed Solution

It is given that two chords are on the opposite sides of the centre in a circle of radius 5 cm, and their lengths are 8 cm and 6 cm respectively.
We have to find the distance between two chords.
Question Image

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

L B = 12 A B = 12 (8) = 4 cm

M D = 12 C D = 12 (6) = 3 cm

For right-angled triangle BLO,
Applying Pythagoras Theorem,

O B 2 = L B 2 + L O 2 ⇒ L O 2 = O B 2 − L B 2 = 52 − 42 = 25 − 16 = 9

LO = 3 cm
For right-angled triangle DMO,
Applying Pythagoras Theorem,

O D 2 = M D 2 + M O 2 ⇒ M O 2 = O D 2 − M D 2 = 52 − 32 = 25 − 9 = 16

OM = 4 cm
Subtracting LO from MO,
MO-LO=4-3
=1cm
So, the distance between the chords is 1 cm.
Therefore, option 1 is correct.

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