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Molodets [167]
2 years ago
5

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

Mathematics
1 answer:
yan [13]2 years ago
8 0

Answer:

\large{\boxed{\sf Chord = 8cm }}

Step-by-step explanation:

First see figure in attachment . As we know that ,<em>P</em><em>e</em><em>r</em><em>p</em><em>e</em><em>n</em><em>d</em><em>i</em><em>c</em><em>u</em><em>l</em><em>a</em><em>r</em><em> </em><em>f</em><em>r</em><em>o</em><em>m</em><em> </em><em>c</em><em>e</em><em>n</em><em>t</em><em>r</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>c</em><em>i</em><em>r</em><em>c</em><em>l</em><em>e</em><em> </em><em>b</em><em>i</em><em>s</em><em>e</em><em>c</em><em>t</em><em>s</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>c</em><em>h</em><em>o</em><em>r</em><em>d</em><em> </em><em>.</em><em> </em>Hence here ,

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

\sf\qquad\longrightarrow AB = 2AC = 2x

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

\sf\qquad\longrightarrow (5cm)^2= x^2+(3cm)^2\\

\sf\qquad\longrightarrow 25cm^2=x^2+9cm^2\\

\sf\qquad\longrightarrow x^2=25cm^2-9cm^2\\

\sf\qquad\longrightarrow x^2=16cm^2\\

\sf\qquad\longrightarrow \pink{ x = 4cm }

Therefore , the length of chord will be ,

\sf\qquad\longrightarrow AB = 2x \\

\sf\qquad\longrightarrow AB = 2(4cm)\\

\sf\qquad\longrightarrow \pink{ AB = 8cm }

<u>H</u><u>e</u><u>n</u><u>c</u><u>e</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>l</u><u>e</u><u>n</u><u>g</u><u>t</u><u>h</u><u> </u><u>o</u><u>f</u><u> </u><u>c</u><u>h</u><u>o</u><u>r</u><u>d</u><u> </u><u>i</u><u>s</u><u> </u><u>8</u><u>c</u><u>m</u><u> </u><u>.</u>

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