please answer these questions

 

Asked by prasutally | 26th May, 2019, 08:20: AM

Expert Answer:

 
In the above figure,
 
O is the cerntre of a circle.
 
OA = 5 cm  ..... radius of outer circle
AC  = 8 cm  ....  chord of outer circle and tangent to the inner circle.
 
To find: OB = ? .....  radius of inner circle
 
OB is perpendicular to AC.  .. (i) ( Tangent is perpendicular to radius at its point of contact)
 
We know  that perpendicular from the centre of circle to the chord bisects the chord.
AB = 4 cm 
 
In ΔOAB,

From (i)
 
By Pythagoras theorem, we get
OB2 = OA2 - AB2
       = 52 - 42
       = 25 - 16
       = 9
→ OB = 3 cm
 

Therefore radius of the inner circle is 3cm.
 
 

 

Answered by Yasmeen Khan | 27th May, 2019, 10:43: AM