Question

2 concentric circles have radii 10cm and 8cm . What is the length of the chord of the bigger circle that touches the smaller circle ?

Answer 1

Answer:

length of chord = 12 cm

Step-by-Step Solution:

To find the length of chord of the bigger circle that touches the smaller circle,if two concentric circles have radii 10cm and 8cm .

See the attached figure,it is clear that chord BC =?

AB= 10 cm

AO= 8 cm

∆ABO is a right triangle at O[By theorem]

here we need to find out the base of the ∆ABO

${AB}^{2} = {OA}^{2} + {OB}^{2} \\ \\ {(10)}^{2} = {(8)}^{2} + {OB}^{2} \\ \\ 100 = 64+ {OB}^{2} \\ \\ 100 - 64 = {OB}^{2} \\ \\ 36 = {OB}^{2} \\ \\ BO = 6 \\ \\ BC = BO + CO \\ \\ BO = CO = 6 \\ \\ BC = 6 + 6 \\ \\ BC = 12 \: cm$

Hope it helps you.