Mathematics
In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.
Circles
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Answer
From figure,
In right-angled triangle OBP,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OB2 = OP2 + BP2
⇒ 202 = 162 + BP2
⇒ 400 = 256 + BP2
⇒ BP2 = 400 - 256
⇒ BP2 = 144
⇒ BP = = 12 cm.
In right-angled triangle AOP,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ OA2 = OP2 + AP2
⇒ 342 = 162 + AP2
⇒ 1156 = 256 + AP2
⇒ AP2 = 1156 - 256
⇒ AP2 = 900
⇒ AP = = 30 cm.
From figure,
AB = AP - BP = 30 - 12 = 18 cm.
Hence, AB = 18 cm.
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