Question

two circles with centres A and B are of radii 6cm and 3 cm respectively if AB is equal to 15 cm find the length of a transverse common tangent to the circles.
Pls solve with diagram and using tangent property of circles

Answer 1

We know that ,

 if d is the distance between the centres of two circles and r1 and r2 are the radii of the circles,

Then,

length of transverse common tangent
 = √[d^2 − (r1+r2)^2]

Now,
 we have,
r1 = 6 cm  
r2 = 3 cm
 d = 15 cm

so,
 length of transverse common tangent 

√[ (15)^2 − (6 + 3)^2]
=√[225 − 81]
=√144
=12 cm

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