Question

The centers of two circles with radii 5 and 7 are 14 units apart. Find the length of the commonexternal tangent.

Answer 1

Since the centers of two circles with radii 5 and 7 are 14 units apart, the length of the common external tangent is equal to
`2 √(13)` units.

In Mathematics and Geometry, Pythagorean theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

`c^2=a^2+b^2`

Where:

• a is the opposite side of a right-angled triangle.
• b is the adjacent side of a right-angled triangle.
• c is the hypotenuse of a right-angled triangle.

In order to determine the length of the common external tangent, we would have to apply Pythagorean's theorem as follows;

`Length \;of\;the\; common\;external \;tangent=√((distance \;between\;centers )^2-(radii\;sum)^2) \\\\Length \;of\;the\; common\;external \;tangent=√((14 )^2-(7+5)^2) \\\\Length \;of\;the\; common\;external \;tangent=√(196-144)\\\\Length \;of\;the\; common\;external \;tangent=√(52)\\\\Length \;of\;the\; common\;external \;tangent=√(4) * √(13) \\\\Length \;of\;the\; common\;external \;tangent=2 √(13) \;units`

Answer 2

Using the pythagoras

`\begin{gathered} x^=√(14^2+2^2) \\ x^=√(200) \\ x=10√(2) \end{gathered}`

The length of the common external tangent is

`10√(2)=\text{ 14.14213}`

The final answer

`\:14.14213`