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?​

Answer 1

$\large \bf \clubs \:  Given :-$

• Radius of Circle = 25 cm

• Distance of its Chord (AB) From Centre (P) = 4cm

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$\large \bf \clubs \:  To \: Find :-$

• Length of Chord

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$\large \bf \clubs \:  Solution :-$

Let ,

• Centre of the circle b = P

• AB is chord

• N is the centre of the chord .

$\bf \large In \: \triangle \: PNB :$

Applying Pythagoras Theorem :

$\bf (PB)^2 = (PN)^2+(NB)^2$

$:\longmapsto {25}^{2} = {4}^{2} + PB^2 = \text{(NB})^2$

$:\longmapsto \text{(NB} {)}^{2} = {25}^{2} - {4}^{2}$

$:\longmapsto \text{(NB)}^2 = 625 - 16$

$\text{(NB)}^2 = 609$

$:\longmapsto \text{NB} = \sqrt{609}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf NB = 24.67 \: cm} }}}$

As N is the midpoint of the chord AB

So ,

$\text{Length of Chord AB = 2NB} \\ \\ = 2 \times 24.67$

Hence,

$\underline \pink{ \underline{\text{ \bf Length of Chord AB = 49.34 cm(approx)}}}$

$\Large\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

☀︎︎ ANSWER ☀︎︎

GIVEN:-

RADIUS OF A CIRCLE = 25cm

AND DISTANCE,d = 4cm

TO FIND:-

THE LENGTH OF CHORD

FORMULA TO FIND THE LENGTH OF CHORD:-

$\sqrt[2]{ {r}^{2} } - {d}^{2}$

SOLUTION:-

LENGTH OF CHORD ,

$= \sqrt[2]{ {25}^{2} } - {4}^{2} \\ \\ = \sqrt[2]{625} - 16 \\ \\ = \sqrt[2]{609} \\ \\ = 2 \times 24.6779253585. \\ \\ =49.355850717$