Two  concentric circles of which radius of larger circle is 13 cm. If the chord of larger circle drawn touching the inner circle is of length 10 cm,find the radius of the inner circle.

Dear Student,

Please find below the solution to the asked query :



Let O be the centre of 2 concentric circles.Let OB be the radius of outer circle and OC be the radius of inner circle.Let AB be the chord of the larger circle that is tangent to inner circle at C.now, AB = 10 cmNow, OCAB  As radius is always  to its tangent at the point of contactNow, we know that perpendicular drawn from the centre to the chord bisects it.So, AC = CB = 5 cmIn OCB,OB2 = OC2 + CB2   Pythagoras theorem132 = OC2 + 52OC2 = 169 - 25 = 144OC = 12 cmSo, radius of inner circle = 12 cm

Hope this would clear your doubt ! 

Do let us know in case of any further concerns. 

Regards 
 

  • 0
What are you looking for?