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Chord AB is 3cm from the center of a circle, the radius of the circle is 5cm, calculate the length of the chord.​

Sagot :

VirαtKσhli

Answer:

[tex]\large{\boxed{\sf Chord = 8cm }}[/tex]

Step-by-step explanation:

First see figure in attachment . As we know that ,Perpendicular from centre of the circle bisects the chord . Hence here ,

  • OC is the perpendicular bisector of chord AB .
  • Let us assume that AC = x , therefore ,

[tex]\sf\qquad\longrightarrow AB = 2AC = 2x [/tex]

Now in ∆OAC , by Pythagoras Theorem , we have ;

[tex]\sf\qquad\longrightarrow (5cm)^2= x^2+(3cm)^2\\ [/tex]

[tex]\sf\qquad\longrightarrow 25cm^2=x^2+9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=25cm^2-9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=16cm^2\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{ x = 4cm } [/tex]

Therefore , the length of chord will be ,

[tex]\sf\qquad\longrightarrow AB = 2x \\ [/tex]

[tex]\sf\qquad\longrightarrow AB = 2(4cm)\\[/tex]

[tex]\sf\qquad\longrightarrow \pink{ AB = 8cm } [/tex]

Hence the length of chord is 8cm .

View image VirαtKσhli
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