find the length of a chord which is at a distance of 12 cm from the centre of the circle with a radius 13cm.
Answers
From the diagram,
AB is a chord
O is the center
OA is the radius
OM is a perpendicular on AB from the center.....................(i)
Given,
Distance of chord from center = 12 cm
Radius = 13cm
Thus, OM = 12 cm
OA = 13 cm
In Triangle OMA,
Angle OMA = 90 degrees (From (i))
Hence, By Pythagoras Theorem,
(OA)^2 = ((OM)^2) + ((MA)^2)
=> 13^2 = (12^2 ) + ((MA)^2)
=> 169 = 144 + ((MA)^2)
=> ((MA)^2=169-144
=> ((MA)^2)=25
=> MA = 5 cm
According to theorem of circle,
If a line is drawn perpendicular to a chord from the center of the circle, then that line divides the chord into two equal halves.
Hence,
According to that,
Length of the required chord = MA * 2
= 5 * 2
=10 cm
