In a circle a chord 2cm away from the centre is 8cm long. What is the length of the chord 3cm away from the centre.
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A chord (say AB) 12 cm is 8 cm away from the center of the circle. What is the length of a chord (say CD) which is 6 cm from the center?
Let the center of the circle be O and E the midpoint of AB. AEO and BEO are both RATs. AE = 12/2 = 6 cm and EO = 8 cm, so R the radius of the circle is [6^2+8^2]^0.5 = (36+64)^0.5 = 100^0.5 = 10 cm.
Now the chord CD is 6 cm from O. Let F be the midpoint of CD. CFO and DFO are both RATs. FO = 6 cm and CO = DO = 10 cm, so CF = DF =[10^2–6^2]^0.5 = (100–36)^0.5 = 64^0.5 = 8 cm, hence CD = 2*8 = 16 cm.
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Step-by-step explanation:
Length of Chord = c = 12cm
distance from centre =d=8cm
radius of circle=r=v(c/2) 2+d2
=v 6^2+8^2 =v36+64 =v100 =10cm
r=10cm
r=10
d=6
C = 2 v10^2-6^2 = 2 v100-64 = 2 v36
= 2x6=12
C=12cm
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