Question

Two circles of radii 17 cm and 8 cm are concentric. the length of a chord of greater circle which touches the smaller circle is

Answer 1

Answer is 30 cm......

Answer 2

$Let \: R \:and \:r \: are \: radii \: of \: two \\concentric \:circles . 'O' \: is \:the \: centre. \\The\: length \: of \: a \:chord \: of \: greater \:circle \\which \: touches \:the \: smaller \:circle \:is \:AB.$

$R = 17 \:cm \: and \: r = 8 \:cm \: ( given)$

$OB \: is \: perpendicular \:to \: AB$

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

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

$OB^{2} = OM^{2} + BM^{2}$

$\implies 17^{2} = 8^{2} + BM^{2}$

$\implies 289 - 64 = BM^{2}$

$\implies 225 = BM^{2}$

$\implies BM = 15 \:cm$

$\red { Length \:of \:the \:Chord (AB)} = 2 \times BM \\= 2 \times 15 \:cm \\\green {= 30 \:cm}$

•••♪