A circle of radius 17m measured 8m from the centre of the circle to the chord? Calculate the length of the chord.

March 22, 2026Mathematics

ScanSolve AI Answer

March 22, 2026

Answer

$2\sqrt{17}~\mathrm{m}$

Step 1: Recall the formula for the length of a chord at a perpendicular distance $d$ from the center of a circle with radius $r$ .

Chord length = 2 \sqrt{r^{2} - d^{2}}

Step 2: Substitute $r = 9$ m and $d = 8$ m into the formula.

Chord length = 2 \sqrt{(9~m)^{2} - (8~m)^{2}}

Step 3: Simplify inside the square root.

(9~m)^{2} = 81~m^{2}

(8~m)^{2} = 64~m^{2}

81~m^{2} - 64~m^{2} = 17~m^{2}

Step 4: Substitute back and simplify.

Chord length = 2 \sqrt{17~m^{2}} = 2 \sqrt{17}~m

2\sqrt{17~m}

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