Question

the figure is a circle with centre O and diameter 20cm.MN-2cm.find length PQ.......... PLEASE HELP ​

Answer 1

$Given \: 'O' \:is \:a \:centre \:of \:a \:circle . \\Diameter (d) = 20\:cm ,\:and \:MN = 2\:cm$

$Radius (r) = OM \\= \frac{d}{2}\\= \frac{20}{2} \\= 10\:cm$

$ON = OM - MN \\= 10\:cm - 2 \:cm \\= 8 \:cm$

$In \:\triangle OPN , \angle {ONP} = 90\degree$

$\underline { \blue { By \: Phythagorean\: theorem:}}$

$OP^{2} = PN^{2} + ON^{2}$

$\implies 10^{2} = PN^{2} + 8^{2}$

$\implies 10^{2} - 8^{2} = PN^{2}$

$\implies 100 - 64 = PN^{2}$

$\implies PN^{2} = 36$

$\implies PN = \sqrt{36} = 6 \:cm$

$Now, Length \:of \: PQ = PN + NQ \\= PN + PN \: ( OM \: bisects \:PQ )$

$= 6 \:cm + 6 \:cm \\= 12 \:cm$

Therefore.,

$\red { Length \:of \: PQ } \green {= 12 \:cm}$

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Answer 2

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