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Question

The length of common chord of two intersecting circles is 30cm. If the diameters of these two circles are 50 cm and 34 cm, Calculate the distance between their centres.

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Solution

length of common chord =30cm=CD
radiusofcircle1=diameters2=5D2=25cm=AC
radiusofcircle2=diameters2=342=17cm=BC
OC=CD2=302=15cm
In triangle ACD
(AD)2+(OC)2=(AC)2
(AO)2=(AC)2(OC)2
=(25)2(15)2=625225=400
AO=20
In a triangle BCO
BO2+OC2=CB2
(BO)2=(CB)2(OC)2
=(17)2(15)2=52×2=64
BO=8cm
distance between centres AB=OB+OA
=8+20
AB=28cm
dostancebetweenthecentreis28cm


1068458_1112453_ans_f96ae30ba6c34211ab42fa55e3805e1e.png

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