Question

two circles with centres A and B of radii 3cm and 4cm intersect at two points C and D such AC and BC are tangents to the two circles find the length of common chord CD​

Answer 1

Answer:

given AC=3cmAC=3cm

and BC=4cmBC=4cm

∴ABC=5cm∴ABC=5cm

Let CP=ycmCP=ycm

and AP=xcmAP=xcm

CP2+AP2=AC2CP2+AP2=AC2

=> y2+x2=9y2+x2=9

=> y2=9−x2y2=9−x2

y2+(5−x)2=16y2+(5−x)2=16

y2=16−(5−x)2y2=16−(5−x)2

y2=16−25−x2+10xy2=16−25−x2+10x

9−x2=−9−x2+10x9−x2=−9−x2+10x

18=10x18=10x

y2=9−(1.8)2y2=9−(1.8)2

=24cm=24cm

CD=4.8cm

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