Question

A circle having a diameter 30 cm has a chord of 24 cm. then the distance of the chord from its center is-​

Answer 1

Answer:

answer-9 cm is distance of the chord from itt center

Answer 2

Answer:

Given :-

• A circle having a diameter of 30 cm has a chord of 24 cm.

To Find :-

• What is the distance of the chord from its center.

Solution :-

First, we have to find the radius of circle :

Given :

• Diameter = 30 cm

As, we know that :

$\clubsuit$ Radius Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}\: \: \: \bigstar$

According to the question by using the formula we get,

$\implies \bf Radius =\: \dfrac{Diameter}{2}$

$\implies \sf Radius =\: \dfrac{\cancel{30}}{\cancel{2}}$

$\implies \sf Radius =\: \dfrac{15}{1}$

$\implies \sf\bold{\purple{Radius =\: 15\: cm}}$

Hence, the radius of circle is 15 cm .

Now, we have to find the distance of the chord from its center :

Given :

• Radius = 15 cm
• Chord of circle = 24 cm = 12 cm

According to the question by using the formula we get,

$\bigstar$ By using Pythagoras Theorem we get,

$\small \implies \sf\bold{\pink{(Distance)^2 =\: (Radius)^2 - (Chord)^2}}$

$\implies \sf (Distance)^2 =\: (15)^2 - (12)^2$

$\implies \sf (Distance)^2 =\: (15 \times 15) - (12 \times 12)$

$\implies \sf (Distance)^2 =\: (225) - (144)$

$\implies \sf (Distance)^2 =\: 225 - 144$

$\implies \sf (Distance)^2 =\: 81$

$\implies \sf Distance =\: \sqrt{81}$

$\implies \sf Distance =\: \sqrt{\underline{9 \times 9}}$

$\implies \sf\bold{\red{Distance =\: 9\: cm}}$

$\therefore$ The distance of the chord from its center is 9 cm .

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