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Shashank Shah

· started a discussion

· 1 Months ago

please help (Question: 293489.0 )

Kindly explain in detail

Question:

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

Options:
A)

2.4 cm

B)

3.6 cm

C)

4.8 cm

D)

6 cm

Solution:

Ans: (c)

  

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
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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