Q4 of 26 Page 79

Radius of a circle with center O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the center of the circle.


Given that


Radius = 41 units


So, OP = 41 units


And PQ = 80 units


We know that a perpendicular drawn from the center of a circle on its chord bisects


the chord.


∴ PM = MQ = 40 cm


In the right angled ΔOAP using Pythagoras theorem,


⇒ OP2 = OM2 + PM2


⇒ 412 = OM2 + 402


⇒ 1681 = OM2 + 1600


⇒ OM2 = 81


⇒ OM = 9 units


So, the distance of chord from the center is 9 units.


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