Question

Find the length of a chord which is at a distance of 5cm from the centre of the circle whose radius is 10cm.

Answer 1

Let the chord be AB and the  centre of the circle is O and the point where the perpendicular from O to the chord=C
OC=5m and OA= 10cm
in ΔOAC,∠C=90degrees
∴By pythagoras theorem,
$OA^{2}= OC^{2} +AC^{2}$
$AC^{2}= OA^{2} - OC^{2}$
$AC^{2}$=$10^{2} - 5^{2}$=100-25=75
AC=√75=5√3cm
since the perpendicular from the centre divides the chord into two equal parts=2*5√3=10√3cm