Question

Two circles of radii 5cm and 3cm with centres O and P touch each other internally. If the perpendicular bisector of the line segment OP meets the circumference of the larger circle at A and B, find the length of AB.

Answer 1

OA = OQ = 5 cm (Radius of bigger circle)

PQ = 3cm       (Radius of smaller circle) 

OP = 2cm 

Perpendicular bisector of OP, i.e. AB meets OP at M. 

OM = MP = `1/2` OP = 1 cm

In right Δ OMA,

By Pythagoras theorem, 

OA² = OM² + MA² 

MA² = 5² -1² 

= 25 - 1 

= 24

AM = `2 sqrt 6` cm

AM = MB = `2 sqrt 6` cm

AB = AM + MB = `2 sqrt 6 + 2 sqrt 6 = 4 sqrt 6`