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 .
