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Home » What will be the length of the chord of a circle in each of the following when:(i) The circle has the radius and the distance of the chord from the center is (ii) The circle of the radius is and the distance of the chord from the center is .
What will be the length of the chord of a circle in each of the following when:(i) The circle has the radius 13cm and the distance of the chord from the center is 12cm(ii) The circle of the radius is 1.7cm and the distance of the chord from the center is 1.5cm.
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What will be the length of the chord of a circle in each of the following when:(i) The circle has the radius 13cm and the distance of the chord from the center is 12cm(ii) The circle of the radius is 1.7cm and the distance of the chord from the center is 1.5cm.

Given: 

Radius =13cm

Distance of chord from the center is 12cm

Therefore, PR=RQ

We know that perpendicular from center to a chord bisects the chord of the circle.

Consider the \vartriangle PRQ,

By using Pythagoras theorem, O{{P}^{2}}=O{{R}^{2}}+P{{R}^{2}}

{{13}^{2}}={{12}^{2}}+P{{R}^{2}}

P{{R}^{2}}={{13}^{2}}-{{12}^{2}}

P{{R}^{2}}=169-144

P{{R}^{2}}=25

PR=\sqrt{25}

PR=5cm

Therefore, length of chord PQ=2PR

=2(5)

=10 cm

Given:

Radius=1.cm

Distance of the chord from the center is 1.5cm

So from figure, PR=RQ

We know perpendicular from center to a chord bisects the chord of the circle.

Consider the \vartriangle PRQ,

Apply Pythagoras theorem, O{{P}^{2}}=O{{R}^{2}}+P{{R}^{2}}

{{\left( 1.7 \right)}^{2}}={{\left( 1.5 \right)}^{2}}+P{{R}^{2}}

P{{R}^{2}}={{\left( 1.7 \right)}^{2}}-{{\left( 1.5 \right)}^{2}}

P{{R}^{2}}=2.89-2.25

P{{R}^{2}}=0.64

PR=\sqrt{0.64}

PR=0.8cm

Therefore, length of chord PQ=2PR

=2(0.8)

=1.6 cm

i

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