Question

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.

Answer 1

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.

Answer 2

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