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प्रश्न
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.
उत्तर
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`
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