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प्रश्न
In the following figure, AD is a straight line, OP ⊥ AD and O is the centre of both circles. If OA = 34cm, OB = 20 cm and OP = 16 cm;
find the length of AB.
उत्तर
For the inner circle, BC is a chord and OP ⊥ BC.
We know that the perpendicular to a chord, from the center of a circle, bisects the chord.
∴ BP = PC
By Pythagoras theorem,
OB2 = OP2 + BP2
⇒ BP2 = 202 - 162 = 144
∴ BP = 12 cm
For the outer circle, AD is the chord and OP ⊥ AD.
We know that the perpendicular to a chord, from the center of a circle, bisects the chord.
∴ AP = PD
By Pythagoras Theorem,
OA2 = OP2 + AP2
⇒ AP2 = (34)2 - (16)2 = 900
⇒ AP = 30 cm
AB = AP - BP = 30 - 12 = 18 cm
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