In a circle of diameter 30 cm a chord of 10cm is drawn. To 2 decimal places, how far is the chord from the center of the circle?

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vijayalalitha vijayalalitha · Answer 1 · 2020-04-10T15:35:27+02:00

Given:

The circle has a diameter of 30 cm and a chord of 10 cm is drawn.

Radius of the circle = 15 cm

Half of the chord = 5 cm

We need to determine the distance of chord from the center of the circle.

Distance of chord from the center of the circle:

Let us use the Pythagorean theorem, to find the distance between the center and the chord.

Let d denote the distance between the center and the chord of the circle.

Thus, we get;

[tex]15^2=d^2+5^2[/tex]

[tex]225=d^2+25[/tex]

[tex]200=d^2[/tex]

Taking square root on both sides, we get;

[tex]14.14=d[/tex]

Thus, the distance between the center and the chord of the circle is 14.14 cm.

Hence, Option A is the correct answer.

ibiscollingwood ibiscollingwood · Answer 2 · 2021-12-07T20:26:39+01:00

The chord is 14.14 cm far from the center of circle.

First option is correct.

The perpendicular drawn from center to the chord, is always divide the chord into two equal parts.

Radius of circle = d/2 = 30/2 = 15 cm

A diagram is attached below, in which distance between center and chord is represented by x .

applying Pythagoras theorem

[tex]x=\sqrt{(15)^{2} -5^{2} }=\sqrt{225-25}=\sqrt{200} =14.14 cm[/tex]

Thus, the chord is 14.14 cm far from the center of circle.

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