Question

A chord 12cm long is 8cm away from the centre of the circle. What is the length of a chord which is 6cm away from the centre.

Answer 1

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 Your answer will come 16.

Answer 2

make a circle which is at the center O draw a chord AB Of 12cm then 1/2AB=6cm & from O oc=8cm then OA =8*8+6*6=√100=10cm draw another chord PQ &OR =6cm PO=10CM then PR=10*10-6*6=√64=8cm SO Length OF PQ=8*2=16 cm(ans.)