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Question
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.
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Solution
Given that,
Radius of circle (OA) = 41cm
Chord (AB) = 80cm
Draw OC⊥AB
We know that
The perpendicular from centre to chord bisects the chord
∴AC=BC=802=40cm
Now in ΔOCA, by Pythagoras theorem
AC2 + OC2 = OA2
=>402 + OC2 = 412
=>1600 + OC2 = 1681
=>OC2 = 81
=> OC2 = 81
=>OC = 81−−√
=>OC = 9cm
Given that,
Radius of circle (OA) = 41cm
Chord (AB) = 80cm
Draw OC⊥AB
We know that
The perpendicular from centre to chord bisects the chord
∴AC=BC=802=40cm
Now in ΔOCA, by Pythagoras theorem
AC2 + OC2 = OA2
=>402 + OC2 = 412
=>1600 + OC2 = 1681
=>OC2 = 81
=> OC2 = 81
=>OC = 81−−√
=>OC = 9cm
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