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Question : If two circles of radii 18 cm and 8 cm touch externally, then the length of a direct common tangent is:

Option 1: 24 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 12 cm


Team Careers360 5th Jan, 2024
Answer (1)
Team Careers360 20th Jan, 2024

Correct Answer: 24 cm


Solution : Let $r{_1}$​ and $r{_2}$​ be the radii of the two circles, and let $d$ be the distance between their centres. In this case:
$d=r{_1}​+r{_2}$​
Given that the radii are 18 cm and 8 cm, we have:
$d=18+8=26$ cm
Now, the direct common tangent is the line segment that joins the points of contact of the two circles. This forms a right-angled triangle with the line segment connecting the centres. The length of the direct common tangent can be found using the Pythagorean theorem.
Let $t$ be the length of the direct common tangent. Then:
$t^2=d^2−(r{_1}​−r{_2}​)^2$
⇒ $t^2=26^2−(18−8)^2$
⇒ $t^2=676−10^2$
⇒ $t^2=676−100$
⇒ $t^2=576$
⇒ $t=24$ cm
Hence, the correct answer is 24 cm.

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