Question

The length of common tangent to the circle of radii $12cm$ and $4cm$ is $15cm$. The distance between their centers is $17cm.$

• A. True
• B. False

Answer 1

The correct option is A True

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 $15cm.$

$CD=15cm$

$CD=BE=15cm$

$AE=AC-CE$

$AE=12-4=8cm$

$AB=xcm$

In the right triangle $BEA,$

Using Pythagoras theorem,

$B{E}^2+E{A}^2=B{A}^2$

$x^2=8^2+{15}^2$

$x^2=289$

$x=17cm$

Hence, the given statement is true.