A chord 16 cm long is 6 cm away from the centre of the circle. Then the chord of length 8 cm is ___ cm away from the centre.
2√21 cm
Given, a chord 16 cm long is 6 cm away from the centre of the circle.
We know, in a circle, the square of half the length of a chord is the difference of the squares of the radius and the perpendicular distance of the chord from the centre of the circle.
Let the radius of the circle be r.
Then, we must have,
(12×16)2=r2−62
⟹64=r2−36
⟹r2=100
⟹r=10 cm
Let the chord of length 8 cm be x cm away from the centre.
Then (12×8)2=r2−x2
⟹16=102−x2
⟹x2=84
⟹x=√84
⟹x=2√21 cm