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Standard X

Mathematics

Arc/Chord Properties of Circles

In a circle o...

Question

In a circle of radius $5 c m, A B$ and $C D$ are two parallel chords of length $8 c m$ and $6 c m$ respectively. Calculate the distance between the chords if they are
On the same side of the centre,

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Solution

$A B = 8 c m \Rightarrow A E = 4 c m C D = 6 m \Rightarrow C F = 3 c m I n △ A E D A E = 4 c m, A O = 5 c m O E = \sqrt{{(A O)}^{2} - {(A E)}^{2}} = \sqrt{5^{2} - 4^{2}} = 3 c m I n △ O F C C F = 3 c m, C O = 5 c m O F = \sqrt{{O C}^{2} - {C F}^{2}} = \sqrt{5^{2} - 3^{2}} = 4 c m$
$∴$ Distance between the chords $= 4 c m - 3 c m = 1 c m$

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In a circle of radius 5 cm,AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords if they are On the same side of the centre,

AB=8cm⇒AE=4cmCD=6m⇒CF=3cmIn△AEDAE=4cm,AO=5cmOE=√(AO)2−(AE)2=√52−42=3cmIn△OFCCF=3cm,CO=5cmOF=√OC2−CF2=√52−32=4cm∴ Distance between the chords=4cm−3cm=1cm

In a circle of radius $5 c m, A B$ and $C D$ are two parallel chords of length $8 c m$ and $6 c m$ respectively. Calculate the distance between the chords if they are
On the same side of the centre,