Question

find the length of a chord which is a distance of 15cm from the centre of a circle of radius of 25cm

Answer 1

Lengh of chord= 40cm

Answer 2

$O \: is \:the \: Centre \:of \:the \:circle.$

$Radius (OA) = OB = 25 \:cm$

$Distance \:of \:chord \: from \: the \:centre (OP)\\ = 15 \:cm$

$Let \: Length \:of \:the \: Chord = AB$

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

$OB^{2} =OP^{2} + PB^{2}$

$\blue {( By \: Phythagorean \: theorem )}$

$\implies 25^{2} = 15^{2} + PB^{2}$

$\implies 625 - 225 = PB^{2}$

$\implies PB^{2} = 400$

$\implies PB= 20 \:cm$

$Now, Length \:of \:the \: chord (AB) = 2 \times AB\\= 2 \times 20 \\= 40 \:cm$

Therefore.,

$\red{Length \:of \:the \: chord} \green {= 40 \:cm }$

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