Question

The length of two parallel chords of a circle are 6cm and 8cm. If the smaller chord is at a distance of 4cm from the centre, what is the distance of the other chord from the centre

Answer 1

this is the answer of this question.

Answer 2

Answer:

The distance of the other chord from the centre of the circle = 3 cm.

To find:

The distance of the other chord from the centre

Solution:

Let the distance of the other chord from the centre be x as shown in figure.

$\begin{array} { c } { \text { In } \Delta \mathrm { MOB } \text { , } } \\\\ { ( O B ) ^ { 2 } = ( O M ) ^ { 2 } + ( M B ) ^ { 2 } } \end{array}$

[According to Pythagoras Theorem]

$O B = \sqrt { 4 ^ { 2 } + 3 ^ { 2 } } = \sqrt { 16 + 9 } = \sqrt { 25 } = 5 \mathrm { cm }$

$\text { In } \Delta \mathrm { NOD }$

[According to Pythagoras Theorem]

$\begin{array} { l } { ( O D ) ^ { 2 } = ( O N ) ^ { 2 } + ( N D ) ^ { 2 } } \\\\ { O N = x = \sqrt { 5 ^ { 2 } - 4 ^ { 2 } } = \sqrt { 25 - 16 } = \sqrt { 9 } = 3 \mathrm { cm } } \end{array}$

Hence, the distance of the other chord from the circle's centre = 3 cm.