Question

The radius of the circle is 13cm and length of one chords is 10 cm .find the distance of the chord from the centre.

Answer 1

Answer:

Step-by-step explanation:

radius=13cm

chord=10cm

1/2chord=5cm

distance=√13^2-5^2

=√169-25=√144=12cm

Answer 2

Answer:

$Distance\:of\:the\: \\chord\: from \: the \: \\centre =OM=12\:cm$

Step-by-step explanation:

$From \: the \: figure:\\</p><p>Radius \: of \: the \: circle (r)=13\:cm ,\\Chord (AB)=10\:cm$

$Let \: distance\:of\:the\: \\chord\: from \: the \: \\centre =OM$

/* By Theorem :

The perpendicular from the centre of a circle to a chord bisects the chord.*/

$In \: Right \: \triangle OMB,\\OB = r = 13 \:cm, \: MB=\frac{AB}{2}\\ = \frac{10}{2}\\=5\:cm$

$OB^{2}=OM^{2}+MB^{2}\\(By\: Pythagorean\:theorem )$

$\implies 13^{2}=OM^{2}+5^{2}$

$\implies 169=OM^{2}+25$

$\implies 169-25=OM^{2}$

$\implies 144=OM^{2}$

$\implies OM=\sqrt{144}$

$\implies OM=\sqrt{12^{2}}$

$\implies OM=12\:cm$

Therefore,

$Distance\:of\:the\: \\chord\: from \: the \: \\centre =OM=12\:cm$

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