Question

Two concentric circles with centre o are given, PAC is a secant and AC is the chord to the larger circle which touches the smaller circle at B if length of tangent CQ is 5 cm, PA=7 cm and op =13 cm and op=13 cm find the radious of the circle at B if length of tangent CQ is 5cm,PA=7cm and op =13cm, finds the radius of the smaller circle.

Answer 1

given : PAC is secant, AC is a chord, CQ = 5 cm PA = 7 cm OP = 13 cm 

to find : OB 

solution; we know that tangents from same exterior point are equal 
                  so, CQ = CB = 5cm 
              we observe that OB is a a perpendicular to chord AC 
              as radius of circle perpendicular to chord bisects the chord
                                    CB=BA = 5 cm
    
      now,in the right triangle OBP 
                     by Pythagoras theorem
 
         OP^2 = OB^2 + PB^2 
           13^2 = OB^2 + (5+7 ) ^2
           OB = 5 cm
hope it helps!!