Question

AB and CD are two parallel chords of a circle whose Centre is o such that AB=30cm AO=OC=17cm OM perpendicular AB and ON perpendicular CD and distance between AB and CD is 23cm.find the length of chord CD​

Answer 1

Step-by-step explanation:

$\blue{ \bf{ \underline{QUESTION} : - }}$

AB and CD are two parallel chords of a circle whose Centre is o such that AB=30cm AO=OC=17cm OM perpendicular AB and ON perpendicular CD and distance between AB and CD is 23cm.find the length of chord CD

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$\boxed{ \huge{ \bold{ Given}}}$

• AB = 30 cm

• AO = 17 cm

• OC = 17 cm

${\boxed{\huge{\bold{ to \: find}}}}$

• Length of Chord CD

$\star{ \pink {\underline{ \underline{Ｓｏｌｕｔｉｏｎ : - }}}}$

We Know that,

AM = 1/2 AB

$\bold{ \sf{AM = \frac{1}{ \cancel{2}}{ \times { \cancel{30}}}}}$

AM = 15 cm

$\huge{ \red{ \sf{ \underline{let}}}}$

OM = x

AND,

ON = 23 - x

____________

(OM) $\sf{ \bold{x = \sqrt{ {AO}^{2} - {AM}^{2} }}}$

$\sf{ \bold{x = \sqrt{ {17}^{2} - {15}^{2} }}}$

$\sf{ \bold{ = \sqrt{284 - 225}}}$

$\sf{ \bold{ = \sqrt{64} = 8}}$

OM = 8 cm

Puting X value in ON ➔

$\bold{ \sf{ON = 23 - x}}$

ON = 23 - 8 = 15 cm

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$\sf{ \bold{ CN = \sqrt{ {OC}^{2} - {ON}^{2} }}}$

$\bold{ \sf{CN = \sqrt{ {17}^{2} - {15}^{2} }}}$

$\sf{ \bold{CN = \sqrt{64} = 8cm}}$

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∴ CD = 2 × CN

= 2 × 8 = 16 cm

CD = 16 cm

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