randamalik85
Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.