There is a circle with an 8-foot chord. The midpoint of the chord is located 3 feet from the center of the circle. What is the length of the diameter of the circle?

Question

anonymous · Answer

Have you read the properties of circles and the Pythagoras' theorem ?

anonymous · Answer

yes math is not my subject

anonymous · Answer

you want the method straight-away ?

anonymous · Answer

i just need help

anonymous · Answer

let me draw the fig for you
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anonymous · Answer

ok

anonymous · Answer

according to a property , the perpendicular bisector of any chord in the circle passes through the centre of the circle. So, the triangle here is a right-angled triangle. Now, can you solve ?

anonymous · Answer

no

anonymous · Answer

yes

anonymous · Answer

is it 8

anonymous · Answer

Now, we can apply the Pythagoras' theorem to this triangle and find out value of r. Then our diameter would be d = 2 x r

anonymous · Answer

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anonymous · Answer

it's not 8. Can you write the Pythagoras' formula ?

anonymous · Answer

its 11

anonymous · Answer

The formula is : $$h^2  = p^2 + b^2$$ where h= hypotenuse of the right traingle, and p, b the perpendicular and base respectively. 

So, here p=4, b=3 then can you find h,( or as in our case r ) ?

anonymous · Answer

Ask me if you didn't get the explanation .

anonymous · Answer

well, you're not responding.  
$$r = \sqrt{4^2 +3^2}$$$$ r = \sqrt{25} = 5$$So, the ans is dia = 2x5 ft =10 ft

anonymous · Answer

thanks