Question

a chord of length 16 cm is drawn in a circle of radius 10 centimetre find the distance of the chord from the centre of the circle

Answer 1

Draw a line from cente to mid of chord,
now there is right angle with
Hypotaneous = 10 cm
P = .?
B = 16/2 = 8 cm
now with pythagoras,
H²=P²+B²
P² = H² - B²
P ² = 10² - 8²
100-64 = 36 cm
P² = 36 cm
P = 6 cm
This is answer

Answer 2

$\huge\bold\red{Question}$

A chord of length 16 cm is drawn in a circle of radius 10 centimetre find the distance of the chord from the centre of the circle.

$\huge\bold\green{Solution}$

$\sf{The \:length \:of \:the\: chord=16\:cm}$

$\sf{The\:radius\: of\: the \:circle = 10\:cm}$

$\sf\color{navy}{When\: a \:perpendicular\: is \:drawn\: on\: the}$ $\sf\color{navy}{chord\: such\: that\: the\: chord\: is\: bisecting\:into}$ $\sf\color{navy}{two.\:Then\: the\: length\: of\: the\:chord\:will\:be}$ $\sf\color{navy}{halved, \:that\: is\: it\: \:becomes \:8cm.}$

$\sf\fcolorbox{gray}{white}{Using\: the\: Pythagorean\: theorem,}$

$\sf{OA^2 = OC^2 + AC^2}$

$\sf{10^2 = OC^2 + 8^2}$

$\sf{100 = OC^2 + 64}$

$\sf{OC^2 = 36}$

$\sf{OC = 6cm}$

$\sf\color{navy}{Therefore,\: the\: distance\: of \:the\: chord\:from}$ $\sf\color{navy}{the\:centre\: of \:the\: circle\: is\: 6cm.}$