Question

O is the centre of two concentric circles ab is a chord of outer circle which touches the inner circle at P and a b equal to 18 cm if the radius of outer circle is 15 cm find the radius of the inner circle​

Answer 1

If Chord AB of Length 18 cm in outer Concentric Circle of Radius 15 cm touches the inner circle then radius of the inner circle​ = 12 cm

Step-by-step explanation:

OA = OB = 15 cm  = Radius of Outer circler

OP = r  = ?  ( Radius of Inner Circle)

As AB Touches Innere circle at P hence

ab is  a tangent

=> AP²  = OA²  - OP²

=> AP² = 15² - r²

Also BP²  = 15² - r²

=> AP² = BP²

=> AP = BP

AP + BP = AB = 18 cm

=> AP = BP = 9 cm

=>  9² = 15² - r²

=> r² = 15² - 9²

=> r² = 225 - 81

=> r² = 144

=> r = 12

the radius of the inner circle​ = 12 cm