O and c are centers of two circles whose radii 13 cm and 3 cm respectively if perpendicular bisector of OC meets on point A and B of the bigger circle then find the length of AB
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A and B are the centres of the circles with radii 5cm and 3cm respectively.
C is the mid-point of AB.
Extend AB upto O point on circumference of outer circle.
AB=AO−BO=5−3=2cm (since AO and BO are radii of larger and smaller circles)
AC=2AB=22=1cm
now in right angled triangle AMP
AC=1cm,AP=5cm
by pythagoras thm.
AP2=PC2+AC2
PC2=AP2−AC2
PC2=52−12
Therefore PQ=2PC=2.24=4.6cm [CP=CQ]
So , option A is the answer.
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