Question

two circles of radii 8 cm and 3 cm have a direct common tangent of length 10 cm. Find the distance between their centres

Answer 1

Answer will be 5√​5
Required distance= 5√​5

Answer 2

Answer: Distance between their centres is 11.18 cm.

Step-by-step explanation:

Since we have given that

Radius of first circle (R) = 8 cm

Radius of second circle (r) = 3 cm

Length of common direct tangent = 10 cm

We need to find the "Distance between their centres":

$\text{Length of direct tangent}=\sqrt{D^2-(R-r)^2}\\\\10=\sqrt{D^2-(8-3)^2}\\\\10^2=D^2-5^2\\\\100+25=D^2\\\\125=D^2\\\\\sqrt{125}=D\\\\5\sqrt{5}=D\\\\D=11.18\ cm$

Hence, Distance between their centres is 11.18 cm.