Question

Calculate the length of a chord which is at a distance 12cm from the centre of a circle of radius 13cm. ​

Answer 1

Your answer is given in attachment

Answer 2

Answer:

$\bullet \: \: \: \: \: \red{\underline{\underline{ \green{\text{Length of the Chord is 10cm}}}}}$

Step-by-step explanation:

Given :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf where \begin{cases} & \sf{radius \: of \: the \: circle = 13cm} \\ \\ & \sf{distance \: from \: the \: centre \: of}\\ & \sf{circle \: to \: chord= 12cm} \end{cases}\end{gathered} \end{gathered} \end{gathered}\end{gathered} \end{gathered}$

To Find :

• the Length of the chord

Solution :

$\underline{ \frak{ \dag \: as \: we \: know}}$

$\\ \boxed{ \pink{ \sf{Pythagorean \: theorem \implies AC² = AB² + BC²}}}$

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$\\ \sf \dashrightarrow13 {}^{2} = 12 {}^{2} + AC²$

$\\ \sf \dashrightarrow169 = 144 + AC²$

$\\ \sf \dashrightarrow \: AC² = 169 - 144$

$\\ \dashrightarrow \sf \: AC = \sqrt{25}$

$\\ \dashrightarrow \sf\: AC = 5$

Now, the Length of the Chord is 2(AC)

ㅤ

⟶ 2(5)

⟶ $\underline{\boxed{\purple{\text{10cm}}}}\star$

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$\underline{\text{Therefore, the Length of the chord is 10cm.}}$