Answer to Question #126885 in Geometry for jungkookiee

Question #126885
A chord of length 12 cm is drawn in a circle of radius 9 cm. Calculate the perpendicular distance from the center of the circle to the chord.
1
Expert's answer
2020-07-19T15:26:26-0400

Consider a circle with center "O" and radius "OA=9\\ cm." Let "AB" be a chord of length "12\\ cm."



We see that "OA" and "OB" are two radii of the circle: "OA=OB=9 \\ cm."

We have the equilateral triangle "\\Delta AOB: OA=OB."

"AD" is the height of the triangle "AOB." Then "AD" is the perpendicular bisector and


"AD=DB={1\\over 2}AB"

Consider the right triangle "OAD"

The Pythagorean Theorem


"OA^2=OD^2+AD^2""OD=\\sqrt{OA^2-AD^2}"

"OA=9 \\ cm, AD=\\dfrac{1}{2}(12\\ cm)=6\\ cm"


"OD=\\sqrt{(9\\ cm)^2-(6\\ cm)^2}=3\\sqrt{5}\\ cm"

The perpendicular distance from the center of the circle to the chord is "3\\sqrt{5}\\ cm."


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Comments

Assignment Expert
19.07.20, 22:26

A solution of the question has already been published.

jungkookiee
19.07.20, 11:31

Why not answered?

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