The length of direct common tangents to two
circles of radii 12 cm and 4 cm is 15 cm.
Calculate the distance between their centres.
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Step-by-step explanation:
Consider two circles of radii 12cm and 4cm with centers B and A respectively.
The length of direct common tangent to both the circles is 15cm.
CD=15 cm
CD=BE=15 cm
AE=AC−CE
AE=12−4=8 cm
AB=x cm
In the right triangle BEA,
Using Pythagoras theorem,
BE
2
+EA
2
=BA
2
x
2
=8
2
+15
2
x
2
=289
x=17 cm
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