Question

hello I am genius in math can anybody also genius in math so please answer this question







radius of a circle is 25 cm and the distance of its chord from the centre is 4 cm what is the length of the chord?
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Answer 1

Step-by-step explanation:

Given :

Radius of a circle is 25 cm.

Distance of its chord from the centre is 4 cm.

To find :

Length of the chord.

Solution :

Finding the perpendicular :-

=> AB = √AO² - BO²

=> AB = √25² - 4²

=> AB = √625 - 16

=> AB = 24.67 cm

Finding the length of chord :-

>> Length of chord = 2(Perpendicular)

=> 2 × 24.67

=> 49.34 cm

• Hence, the length of chord of the circle is 49.34 cm.

Answer 2

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${\maltese \; {\underline{\underline{\textsf{\textbf{Given that :}}}}}}$

• The radius of a circle measures 25cm
• The chord of the circle is at a distance of 4cm

${\maltese \; {\underline{\underline{\textsf{\textbf{To Find :}}}}}}$

• The total length of the chord made in the circle

${\maltese \; {\underline{\underline{\textsf{\textbf{Assumptions :}}}}}}$

• Let the total length  of the chord be 2x
• Let half of the length of the chord be x

${\maltese \; {\underline{\underline{\textsf{\textbf{Required Solution :}}}}}}$

➤ Now let's  make a figure such that it satisfies the given statements in the question and this would be helpful in figuring out the answer in a easier way [ As shown in the attachment ]

★ Now we observe that a right- angled triangle ( Δ AOB ) is formed where the length of 2 of its sides are known and the length of it's third side equals to half the length of the chord

✸ Now let's use  Pythagoras Theorem and find the measure of the third side of the triangle and then double it's measure to find the length of the chord of the circle ;

* Pythagoras Theorem :

Pythagoras theorem states the relation between the sides of a right angled triangle where the square of its hypotenuse equals to the sums of squares of its other two sides

$\bigstar \; {\underline{\boxed{\bf {Hypotenuse^2 = Base^2 + Side^2 }}}}$  

Here in the triangle formed joining the chord to the radius with a line segment measuring 4cm is to be considered as Δ AOB where ,

• Base of of the triangle ( AB ) = x units
• Hypotenuse of the triangle ( OB ) = 25cm
• Other Side of the triangle ( OA ) = 4cm

By applying the values we get the result ,

$\sf {: \implies } ( OB ) ^2 = \bf ( AB ) ^2 + ( OA) ^2$

$\sf {: \implies } ( AB ) ^2 = \bf ( OB ) ^2 - ( OA) ^2$

$\sf {: \implies } ( AB ) ^2 = \bf ( 25 ) ^2 - ( 4) ^2$

$\sf {: \implies } ( AB ) ^2 = \bf 625 - 16$

$\sf {: \implies } ( AB ) ^2 = \bf 625 - 16$

$\sf {: \implies } ( AB ) ^2 = \bf 609$

$\sf {: \implies } ( AB ) = \bf \sqrt{ 609 }$

$\sf {: \implies } ( AB ) = \bf 24.67$

✒ AB = 24.67 cm

Now we know that the length of thee chord would be 2 times of "x" ' here x is the value of AB which is 24.67 now let's multiply the resultant with 22 to find the measure of the chords

$\therefore {\underline{\boxed{\tt{Length \; of \;2 AB = 49.34cm }}}}$

${\maltese \; {\underline{\underline{\textsf{\textbf{Therefore :}}}}}}$

• The length of the chord in thee circle equals to 49.34cm

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