If the perpendicular from chord is x, the length of cord is 11.3 and diameter be 15.5 then the value of x is 4.54.
Given Perpendicular from center to chord is x. The length of cord be 11.3 and the diameter be 15.5.
Perpendicular means a line on other line making an angle of 90 degrees. Cord is the length of line joining two points on a circle and is different from radius or diameter. We know that the formula of calculating the length of chord is as under:
l=[tex]2\sqrt{r^{2} -d^{2} }[/tex]
now put the value of l=11.3 and r=15.5/2=7.25
11.3=[tex]2\sqrt{7.25^{2} -x^{2} }[/tex]
11.3/2=[tex]\sqrt{52.5625-x^{2} }[/tex]
5.65=[tex]\sqrt{52.5625-x^{2} }[/tex]
squaring both sides
[tex]5.65^{2} =52.5625-x^{2}[/tex]
31.9225=52.5625-[tex]x^{2}[/tex]
31.9225-52.5625=-[tex]x^{2}[/tex]
-20.64=-[tex]x^{2}[/tex]
20.64=[tex]x^{2}[/tex]
x=4.54
Hence if the length of cord is 11.3 and diameter is 15.5 then the value of x is 4.54.
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