Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.
Answers
Given : A chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.
Let the distance of the chord from the centre , OC = 4 cm and Radius of the circle, OA = 6 cm
In ΔOCA, by using Pythagoras theorem
OA² = AC² + OC²
6² = AC² + 4²
36 = AC² + 16
AC² = 36 - 16
AC² = 20
AC = √20
AC = √(5 × 4)
AC = 2√5
AC = 2 × 2.23
AC = 4.47 cm
We know that,the perpendicular from centre to chord bisects the chord.
∴ AC = BC = 4.47 cm
Then,
Chord AB = AC + BC
Chord AB = 4.47 + 4.47
Chord AB = 8.94 cm
Hence, the length of a chord is 8.94 cm
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Answer:-
Given :
A chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.
Let the distance of the chord from the centre , OC = 4 cm and Radius of the circle, OA = 6 cm
In ΔOCA, by using Pythagoras theorem
OA² = AC² + OC²
6² = AC² + 4²
36 = AC² + 16
AC² = 36 - 16
AC² = 20
AC = √20
AC = √(5 × 4)
AC = 2√5
AC = 2 × 2.23
AC = 4.47 cm
We know that,the perpendicular from centre to chord bisects the chord.
∴ AC = BC = 4.47 cm
Then,
Chord AB = AC + BC
Chord AB = 4.47 + 4.47
Chord AB = 8.94 cm
Hence, the length of a chord is 8.94 cm
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