Diameter of a circle

Diameter of a circle

Postby AugustineCampbell » Fri Feb 01, 2019 8:24 am


How to find the diameter of a circle, knowing the chord and the distance from the center of the circle to the chord?
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Re: Diameter of a circle

Postby Baltuilhe » Mon Feb 04, 2019 12:39 pm

Good afternoon!!

If Radius of the circle R, Chord measure is C and distance from the center of the circle to the chord is D:
[tex]R^2=\left(\dfrac{C}{2}\right)^2+D^2\\\\\boxed{R=\sqrt{\left(\dfrac{C}{2}\right)^2+D^2}}[/tex]

Knowing R, you have the diameter.

I hope I have helped!

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Re: Diameter of a circle

Postby HallsofIvy » Sat Mar 30, 2019 1:19 pm

Just to clarify Baltuilhe's post- Draw a line from the center of the circle to the midpoint of the chord and another from the center of the circle to an endpoint of the chord. It is simple geometry that the line to the midpoint of the chord is perpendicular to the chord so we have a right triangle with the radius of the circle, R, as hypotenuse, the distance from the center, D, as the length of one leg, and half the length of the chord, C/2, as the length of the other leg. Then the Pythagorean Theorem gives (D)^2+ (C/2)^2= R^2.

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